Continuum Theory Gem Award

(A) 1883-2022 setup of winners SORTED BY YEAR


1883	Cantor	G.	Continuum is a compact playground for any small ant.
1887	Jordan	C.	Each simple closed planar curve surrounds its inside and outside.
1890	Peano	G.	Drawing a full square with a segment.
1900	Hilbert	D.	Hilbert cube containing a copy of any continuum.
1902	Painleve	P.	A decreasing sequence of continua forms a continuum.
1910	Brouwer	L.E.J.	Buckethandle as the simplest indecomposable continuum. 
1912	Janiszewski	Z.	Arc-less continuum.
1912	Janiszewski	Z.	Buckethandle in an angular shape.
1912	Wada	T.	Lakes of Wada (three disjoint connected open sets of the plane with the same boundary).
1914	Hahn	H.	Locally connected continuum is a continuous image of [0,1].
1914	Mazurkiewicz	S.	Sierpinski carpet contains only ramification points of infinite order.
1915	Sierpinski	W.	Half homogeneous Sierpinski carpet containing a copy of every planar curve.
1915	Sierpinski	W.	Sierpinski triangle with only ramification points.
1916	Moore	R.L.	Chainable continuum.
1918	Sierpinski	W.	Any continuum is sigma connected, not a countable union of disjoint closed sets.
1918	Janiszewski	Z.	Foundation of Fundamenta Mathematicae journal (with W. Sierpinski and S. Mazurkiewicz). 
1920	Antoine	L. 	Antoine's necklace (wild embedding of the Cantor set).
1920	Mazurkiewicz	S.	Locally connected continuum is a continuous image of [0,1].
1920	Moore	R.L.	Two non-cut points in any continuum.
1922	Antoine	L. 	Antoine's arc (wild embedding of the arc).
1922	Knaster	B.	Buckethandle in a round shape.
1922	Knaster	B.	Pseudo-arc, the nondegenerate hereditarily indecomposable continuum.
1923	Wazewski	T.	Wazewski universal dendrite containing a copy of any dendrite.
1924	Alexander	J.W.	Alexander horned sphere, a wild embedding of a sphere into space.
1924	Mazurkiewicz	S.	Each locally connected homogeneous plane continuum is a simple closed curve.
1925	Gehman	H.M.	Dendrite with ramification points of order 3 and end points forming the Cantor set.
1926	Menger	K.	Homogeneous Menger sponge containing a copy of every curve.
1927	Kuratowski	K.	A point of irreducibility in a continuum is not contained in two proper subcontinua (a characterization).
1927	Vietoris	L.	Solenoid (in a sequence folding tube in a previous tube twice).
1929	Roberts	J.H.	Upper semicontinuous decomposition of the plane into nonseparating locally connected subcontinua.
1930	Mazurkiewicz	S.	A typical continuum is hereditarily indecomposable.
1930	Dantzig	D. von	Homogeneity of a solenoid.
1930	Kurtowski	K.	Planability test for local dendrites (cannot contain two special continua).
1930	Whyburn	G.T.	Whyburn's curve, a continuum every subcontinuum of which separates the plane.
1931	Keller	O.H.	Hilbert cube is homogeneous.
1932	Miller	E.W.	A dendrite not containing its proper copy.
1932	Waraszkiewicz	Z.	Waraszkiewicz's spirals ( an uncountable family of continuously incomparable planar curves).
1934	Borsuk	K.	The dunce hat (Borsuk's tube, acyclic polyhedron which is not the union of two acyclic polyhedra).
1935	Mazurkiewicz	S. 	Any compact metric space of dimension 2 contains a nondegenerate indecomposable continuum.
1936	Whyburn	G.T.	Decomposition of 3-space into 3-space using Antoine's arc and points.
1937	Sierpinski	W.	Arc mapped onto Hilbert cube. 
1937	Freudenthal	H.	Solenoid as an inverse limit.
1937	Claytor	S.	Two Claytor continua block planarity of a Peano continuum.  
1944	Sorgenfrey	R.H.	Every nondegenerate unicoherent continuum which is not a triod is irreducible.
1945	Besicovitch	A.S.	A dendrite such that no two of its open sets are homeomorphic.
1947	Borsuk	K.	An example of a simple arc in space whose projection in every plane has interior points.
1948	Bing 	R.H.	Homogeneity of the pseudo-arc.
1948	Moise	E.E.	Indecomposable planar continuum homeomorphic to each of its nondegenerate subcontinua (the pseudo-arc).
1948	Jones	F. B.	T function (the complement of T(A) contains the interior points of subcontinua not meeting A).
1951	Hamilton	O.H.	Each chainable continuum has the fixed-point property.
1951	Bing	R.H.	Planar non-chainable circularly chainable hereditarily indecomposable continuum (a pseudo-circle).
1952	Anderson	R.D.	A continuous decomposition of the plane into nonseparating subcontinua.
1958	Anderson	R.D.	Menger universal curve is homogeneous.
1959	Anderson	R.D.	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1959	Choquet	G.	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1959	Isbell	J.R.	Chainable continuum is an inverse limit of an inverse sequence of arcs.
1959	Bing 	R.H.	The circle of pseudo-arcs.
1959	Jones	F. B.	The circle of pseudo-arcs.
1961	Lelek	A.	The Lelek fan (a smooth fan with a dense set of endpoints).
1962	Lelek	A.	Weakly chainable continua are exactly continuous images of the pseudo-arc.
1963	Borsuk 	K.	Borsuk nonplanar fan.
1964	Henderson	G.	Arc is the only decomposable hereditarily equivalent continuum.
1964	Lelek	A.	Span zero (no two points can change the position on a continuum).
1964	Henderson	G.	The pseudo-arc is an inverse limit using only one binding map.
1964	Charatonik	J.J.	Unicoherence of locally connected continua is an invariant under confluent mappings.
1965	Effros	E.G.	The group of homeomorphisms acts locally.
1965	Schori	R.M.	Universal chainable continuum.
1967	Smale	S. 	Buckethandle in a horseshoe shape as the fixed set of a mapping square into a horseshoe.
1967	Cook	H.	Cook's continuum (a continuum admitting only the identity or a constant mapping onto itself).
1969	Krasinkiewicz	J.	Sierpinski universal plane curve is 1/2-homogeneous.
1970	Rogers	J.T.	A pseudo-solenoid  is a common model for circle-like continua.
1970	Rogers	J.T.	The pseudo-circle is not homogeneous.
1970	Fearnley	L.	The pseudo-circle is unique.
1971	Lelek	A.	Houston problem book.
1972	Ingram	W.T.	An atriodic tree-like continuum with positive span.
1972	Bennett	R.B.	Menger universal curve is countable dense homogeneous.
1972	Charatonik	J.J.	Problem posing (?) challenge over problem solving (exists) and generalisations (for all).
1973	Nadler	Sam B. Jr.	The indecomposability of the dyadic solenoid.
1974	Rosenholtz	I.	Open image of a chainable continuum is chainable.
1975	Ungar	G.S.	2-homogeneous continuum is locally connected.
1977	Hagopian	Ch.L.	Solenoids (homogeneous continua with only arc subcontinua).
1977	Rogers	J.T.	Solenoids of pseudo-arcs.
1978	Charatonik	J.J.	Arc-like openly homogenous continuum is the pseudo-arc.
1978	Curtis	D.W.	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1978	Schori	R.M.	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1978	Illanes	A.	Hyperspaces of sets. Book I 
1978	Grispolakis	J.	Universal smooth dendroid.
1978	Tymchatyn	E.D.	Universal smooth dendroid.
1979	Bellamy	D.P.	A nonplanar tree-like continuum which admits a fixed point free mapping.
1979	Ingram	W.T.	Hereditarily indecomposable tree-like continua.
1980	Krasinkiewicz	J.	A dendroid with a monotone open map onto an arc.
1980	Minc	P.	A dendroid with a monotone open map onto an arc.
1980	Oversteegen	Lex G.	A dendroid with a monotone open map onto an arc.
1980	Mill	J. van	A Peano continuum homeomorphic to its own square but not to its countable infinite product.
1980	Iliadis	S.D.	Universal completely regular continuum (each nondegenerate subcontinuum has a nonempty interior).
1982	Oversteegen	Lex	Indecomposable homogeneous planar continuum has span zero.
1982	Tymchatyn	E.D.	Indecomposable homogeneous planar continuum has span zero.
1984	Charatonik	J.J.	Example of a smooth dendroid without ordinary points.
1984	Nikiel	J.	Gehman dendroid is the only dendrite with its set of end-points homeomorphic to the Cantor set.
1985	Mackowiak	T.	A universal hereditarily indecomposable continuum.
1986	Kennedy	J.	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1986	Rogers	J.T.	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1988	Mackowiak	T.	A characterization of finitely irreducible continua.
1989	Charatonik	J.J.	A fan is smooth iff can be embedded into the Cantor fan.
1989	Charatonik	W.J.	A fan is smooth iff can be embedded into the Cantor fan.
1989	Charatonik	W.J.	Lelek fan is the unique smooth fan with a dense set of endpoints.
1990	Kuperberg	K.	A locally connected homogeneous non-bihomogeneous continuum of dimension 7.
1990	Krupski	P.	Homogeneous tree-like continua are hereditarily indecomposable.
1990	Prajs	J.R.	Homogeneous tree-like continua are hereditarily indecomposable.
1991	Minc	P.	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1991	Transue	W.R.R.	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1992	Nadler	Sam B. Jr.	Continuum Theory. An Introduction. Book II
1993	Nadler	Sam B. Jr.	A continuum separated by each of its nondegenerate proper subcontinua.
1993	Seldomridge	Gary A.	A continuum separated by each of its nondegenerate proper subcontinua.
1993	Bellamy	D.	A tree-like continuum without the fixed-point property.
1993	Minc	P.	An atriodic simple-4-od-like continuum which is not simple-triod-like.
1993	Aarts	J.M.	Hairy arc.
1993	Oversteegen	L.G.	Hairy arc.
1994	Bandt	Ch.	Non-zero composants of the Buckethandle are homeomorphic.
1995	Kennedy	J.	Buckethandle as an inverse limit of circles using a single bonding map.
1996	Hagopian	Ch. L.	Simply connected plane continua have the fixed-point property.
1999	Lewis	W.	An example of a chainable continuum that admits an exactly 2-to-1 mapping onto a continuum.
1999	Illanes	A.	Hyperspaces. Book III
1999	Nadler	Sam B. Jr.	Hyperspaces. Book III
1999	Lewis	W.	Pseudo-arc maturity.
1999	Illanes	A.	The Continuum theory hyperspace in Mexico.
1999	Minc	P.	There exists a tree-like weakly chainable continuum without the fixed-point property.
2000	Prajs	J.R.	A continuous decomposition of the Menger curve into pseudo-arcs.
2002	Illanes	A.	Buckethandle admits no mean.
2003	Minc	P.	Buckethandle is mapped onto a planar dedroid with point-inverses at most of cardinality 3.
2003	Minc	P.	Planar dendroid contains a single point bottleneck.
2005	Macias	S.	Topics on continua. Book IV
2010	Illanes	A.	The arc is the only chainable continuum admitting a mean.
2010	Villanueva	H.	The arc is the only chainable continuum admitting a mean.
2011	Hoehn	L.C.	A non-chainable plane continuum with span zero.
2012	Ingram	W.T.	Inverse limit of books on inverse limit...
2013	Vejnar	B.	Acrless-arc, the arc-like arc-less continuum with two endpoints.
2013	Hoehn	L.C.	An uncountable collection of copies of a non-chainable tree-like continuum in the plane.
2014	Sturm	F. 	Pseudo-solenoid is not continuously homogeneous.
2015	Mill	J. van	Pseudo-arc is the only continuum with homeomorphically near property.
2015	Banic	I.	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
2015	Martinez-de-la-Vega	V.	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
2016	Prajs	J.R.	Arcwise connected homogeneous continuum is a continuous image of the Cantor fan.
2016	Hoehn	L.C.	Classification of planar homogeneous continua.
2016	Oversteegen	Lex	Classification of planar homogeneous continua.
2016	Vejnar	B.	Two non-block points in any continuum.
2020	Hoehn	L.C.	Classification of hereditarily equivalent plane continua.
2020	Oversteegen	Lex	Classification of hereditarily equivalent plane continua.

(B) 1883-2022 setup of winners SORTED BY NAME

1993	Aarts	J.M.	Hairy arc.
1924	Alexander	J.W.	Alexander horned sphere, a wild embedding of a sphere into space.
1952	Anderson	R.D.	A continuous decomposition of the plane into nonseparating subcontinua.
1958	Anderson	R.D.	Menger universal curve is homogeneous.
1959	Anderson	R.D.	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1920	Antoine	L. 	Antoine's necklace (wild embedding of the Cantor set).
1922	Antoine	L. 	Antoine's arc (wild embedding of the arc).
1994	Bandt	Ch.	Non-zero composants of the Buckethandle are homeomorphic.
2015	Banic	I.	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
1993	Bellamy	D.	A tree-like continuum without the fixed-point property.
1979	Bellamy	D.P.	A nonplanar tree-like continuum which admits a fixed point free mapping.
1972	Bennett	R.B.	Menger universal curve is countable dense homogeneous.
1945	Besicovitch	A.S.	A dendrite such that no two of its open sets are homeomorphic.
1951	Bing	R.H.	Planar non-chainable circularly chainable hereditarily indecomposable continuum (a pseudo-circle).
1948	Bing 	R.H.	Homogeneity of the pseudo-arc.
1959	Bing 	R.H.	The circle of pseudo-arcs.
1934	Borsuk	K.	The dunce hat (Borsuk's tube, acyclic polyhedron which is not the union of two acyclic polyhedra).
1947	Borsuk	K.	An example of a simple arc in space whose projection in every plane has interior points.
1963	Borsuk 	K.	Borsuk nonplanar fan.
1910	Brouwer	L.E.J.	Buckethandle as the simplest indecomposable continuum. 
1883	Cantor	G.	Continuum is a compact playground for any small ant.
1937	Claytor	S.	Two Claytor continua block planarity of a Peano continuum.  
1967	Cook	H.	Cook's continuum (a continuum admitting only the identity or a constant mapping onto itself).
1978	Curtis	D.W.	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1930	Dantzig	D. von	Homogeneity of a solenoid.
1965	Effros	E.G.	The group of homeomorphisms acts locally.
1970	Fearnley	L.	The pseudo-circle is unique.
1937	Freudenthal	H.	Solenoid as an inverse limit.
1925	Gehman	H.M.	Dendrite with ramification points of order 3 and end points forming the Cantor set.
1978	Grispolakis	J.	Universal smooth dendroid.
1996	Hagopian	Ch. L.	Simply connected plane continua have the fixed-point property.
1977	Hagopian	Ch.L.	Solenoids (homogeneous continua with only arc subcontinua).
1914	Hahn	H.	Locally connected continuum is a continuous image of [0,1].
1951	Hamilton	O.H.	Each chainable continuum has the fixed-point property.
1964	Henderson	G.	Arc is the only decomposable hereditarily equivalent continuum.
1964	Henderson	G.	The pseudo-arc is an inverse limit using only one binding map.
1900	Hilbert	D.	Hilbert cube containing a copy of any continuum.
2011	Hoehn	L.C.	A non-chainable plane continuum with span zero.
2013	Hoehn	L.C.	An uncountable collection of copies of a non-chainable tree-like continuum in the plane.
2016	Hoehn	L.C.	Classification of planar homogeneous continua.
2020	Hoehn	L.C.	Classification of hereditarily equivalent plane continua.
1964	Charatonik	J.J.	Unicoherence of locally connected continua is an invariant under confluent mappings.
1972	Charatonik	J.J.	Problem posing (?) challenge over problem solving (exists) and generalisations (for all).
1978	Charatonik	J.J.	Arc-like openly homogenous continuum is the pseudo-arc.
1984	Charatonik	J.J.	Example of a smooth dendroid without ordinary points.
1989	Charatonik	J.J.	A fan is smooth iff can be embedded into the Cantor fan.
1989	Charatonik	W.J.	A fan is smooth iff can be embedded into the Cantor fan.
1989	Charatonik	W.J.	Lelek fan is the unique smooth fan with a dense set of endpoints.
1959	Choquet	G.	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1980	Iliadis	S.D.	Universal completely regular continuum (each nondegenerate subcontinuum has a nonempty interior).
1978	Illanes	A.	Hyperspaces of sets. Book I 
1999	Illanes	A.	Hyperspaces. Book III
1999	Illanes	A.	The Continuum theory hyperspace in Mexico.
2002	Illanes	A.	Buckethandle admits no mean.
2010	Illanes	A.	The arc is the only chainable continuum admitting a mean.
1972	Ingram	W.T.	An atriodic tree-like continuum with positive span.
1979	Ingram	W.T.	Hereditarily indecomposable tree-like continua.
2012	Ingram	W.T.	Inverse limit of books on inverse limit...
1959	Isbell	J.R.	Chainable continuum is an inverse limit of an inverse sequence of arcs.
1912	Janiszewski	Z.	Arc-less continuum.
1912	Janiszewski	Z.	Buckethandle in an angular shape.
1918	Janiszewski	Z.	Foundation of Fundamenta Mathematicae journal (with W. Sierpinski and S. Mazurkiewicz). 
1948	Jones	F. B.	T function (the complement of T(A) contains the interior points of subcontinua not meeting A).
1959	Jones	F. B.	The circle of pseudo-arcs.
1887	Jordan	C.	Each simple closed planar curve surrounds its inside and outside.
1931	Keller	O.H.	Hilbert cube is homogeneous.
1986	Kennedy	J.	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1995	Kennedy	J.	Buckethandle as an inverse limit of circles using a single bonding map.
1922	Knaster	B.	Buckethandle in a round shape.
1922	Knaster	B.	Pseudo-arc, the nondegenerate hereditarily indecomposable continuum.
1969	Krasinkiewicz	J.	Sierpinski universal plane curve is 1/2-homogeneous.
1980	Krasinkiewicz	J.	A dendroid with a monotone open map onto an arc.
1990	Krupski	P.	Homogeneous tree-like continua are hereditarily indecomposable.
1990	Kuperberg	K.	A locally connected homogeneous non-bihomogeneous continuum of dimension 7.
1927	Kuratowski	K.	A point of irreducibility in a continuum is not contained in two proper subcontinua (a characterization).
1930	Kurtowski	K.	Planability test for local dendrites (cannot contain two special continua).
1961	Lelek	A.	The Lelek fan (a smooth fan with a dense set of endpoints).
1962	Lelek	A.	Weakly chainable continua are exactly continuous images of the pseudo-arc.
1964	Lelek	A.	Span zero (no two points can change the position on a continuum).
1971	Lelek	A.	Houston problem book.
1999	Lewis	W.	An example of a chainable continuum that admits an exactly 2-to-1 mapping onto a continuum.
1999	Lewis	W.	Pseudo-arc maturity.
2005	Macias	S.	Topics on continua. Book IV
1985	Mackowiak	T.	A universal hereditarily indecomposable continuum.
1988	Mackowiak	T.	A characterization of finitely irreducible continua.
2015	Martinez-de-la-Vega	V.	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
1914	Mazurkiewicz	S.	Sierpinski carpet contains only ramification points of infinite order.
1920	Mazurkiewicz	S.	Locally connected continuum is a continuous image of [0,1].
1924	Mazurkiewicz	S.	Each locally connected homogeneous plane continuum is a simple closed curve.
1930	Mazurkiewicz	S.	A typical continuum is hereditarily indecomposable.
1935	Mazurkiewicz	S. 	Any compact metric space of dimension 2 contains a nondegenerate indecomposable continuum.
1926	Menger	K.	Homogeneous Menger sponge containing a copy of every curve.
1980	Mill	J. van	A Peano continuum homeomorphic to its own square but not to its countable infinite product.
2015	Mill	J. van	Pseudo-arc is the only continuum with homeomorphically near property.
1932	Miller	E.W.	A dendrite not containing its proper copy.
1980	Minc	P.	A dendroid with a monotone open map onto an arc.
1991	Minc	P.	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1993	Minc	P.	An atriodic simple-4-od-like continuum which is not simple-triod-like.
1999	Minc	P.	There exists a tree-like weakly chainable continuum without the fixed-point property.
2003	Minc	P.	Buckethandle is mapped onto a planar dedroid with point-inverses at most of cardinality 3.
2003	Minc	P.	Planar dendroid contains a single point bottleneck.
1948	Moise	E.E.	Indecomposable planar continuum homeomorphic to each of its nondegenerate subcontinua (the pseudo-arc).
1916	Moore	R.L.	Chainable continuum.
1920	Moore	R.L.	Two non-cut points in any continuum.
1973	Nadler	Sam B. Jr.	The indecomposability of the dyadic solenoid.
1992	Nadler	Sam B. Jr.	Continuum Theory. An Introduction. Book II
1993	Nadler	Sam B. Jr.	A continuum separated by each of its nondegenerate proper subcontinua.
1999	Nadler	Sam B. Jr.	Hyperspaces. Book III
1984	Nikiel	J.	Gehman dendroid is the only dendrite with its set of end-points homeomorphic to the Cantor set.
1993	Oversteegen	L.G.	Hairy arc.
1982	Oversteegen	Lex	Indecomposable homogeneous planar continuum has span zero.
2016	Oversteegen	Lex	Classification of planar homogeneous continua.
2020	Oversteegen	Lex	Classification of hereditarily equivalent plane continua.
1980	Oversteegen	Lex G.	A dendroid with a monotone open map onto an arc.
1902	Painleve	P.	A decreasing sequence of continua forms a continuum.
1890	Peano	G.	Drawing a full square with a segment.
1990	Prajs	J.R.	Homogeneous tree-like continua are hereditarily indecomposable.
2000	Prajs	J.R.	A continuous decomposition of the Menger curve into pseudo-arcs.
2016	Prajs	J.R.	Arcwise connected homogeneous continuum is a continuous image of the Cantor fan.
1929	Roberts	J.H.	Upper semicontinuous decomposition of the plane into nonseparating locally connected subcontinua.
1970	Rogers	J.T.	A pseudo-solenoid  is a common model for circle-like continua.
1970	Rogers	J.T.	The pseudo-circle is not homogeneous.
1977	Rogers	J.T.	Solenoids of pseudo-arcs.
1986	Rogers	J.T.	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1974	Rosenholtz	I.	Open image of a chainable continuum is chainable.
1993	Seldomridge	Gary A.	A continuum separated by each of its nondegenerate proper subcontinua.
1965	Schori	R.M.	Universal chainable continuum.
1978	Schori	R.M.	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1915	Sierpinski	W.	Half homogeneous Sierpinski carpet containing a copy of every planar curve.
1915	Sierpinski	W.	Sierpinski triangle with only ramification points.
1918	Sierpinski	W.	Any continuum is sigma connected, not a countable union of disjoint closed sets.
1937	Sierpinski	W.	Arc mapped onto Hilbert cube. 
1967	Smale	S. 	Buckethandle in a horseshoe shape as the fixed set of a mapping square into a horseshoe.
1944	Sorgenfrey	R.H.	Every nondegenerate unicoherent continuum which is not a triod is irreducible.
2014	Sturm	F. 	Pseudo-solenoid is not continuously homogeneous.
1991	Transue	W.R.R.	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1978	Tymchatyn	E.D.	Universal smooth dendroid.
1982	Tymchatyn	E.D.	Indecomposable homogeneous planar continuum has span zero.
1975	Ungar	G.S.	2-homogeneous continuum is locally connected.
2013	Vejnar	B.	Acrless-arc, the arc-like arc-less continuum with two endpoints.
2016	Vejnar	B.	Two non-block points in any continuum.
1927	Vietoris	L.	Solenoid (in a sequence folding tube in a previous tube twice).
2010	Villanueva	H.	The arc is the only chainable continuum admitting a mean.
1912	Wada	T.	Lakes of Wada (three disjoint connected open sets of the plane with the same boundary).
1932	Waraszkiewicz	Z.	Waraszkiewicz's spirals ( an uncountable family of continuously incomparable planar curves).
1923	Wazewski	T.	Wazewski universal dendrite containing a copy of any dendrite.
1930	Whyburn	G.T.	Whyburn's curve, a continuum every subcontinuum of which separates the plane.
1936	Whyburn	G.T.	Decomposition of 3-space into 3-space using Antoine's arc and points.

(C) 1883-2022 setup of winners SORTED BY YEAR with separators ";" for importing into spreadsheet:

1883	;	Cantor	;	G.	;	Continuum is a compact playground for any small ant.
1887	;	Jordan	;	C.	;	Each simple closed planar curve surrounds its inside and outside.
1890	;	Peano	;	G.	;	Drawing a full square with a segment.
1900	;	Hilbert	;	D.	;	Hilbert cube containing a copy of any continuum.
1902	;	Painleve	;	P.	;	A decreasing sequence of continua forms a continuum.
1910	;	Brouwer	;	L.E.J.	;	Buckethandle as the simplest indecomposable continuum. 
1912	;	Janiszewski	;	Z.	;	Arc-less continuum.
1912	;	Janiszewski	;	Z.	;	Buckethandle in an angular shape.
1912	;	Wada	;	T.	;	Lakes of Wada (three disjoint connected open sets of the plane with the same boundary).
1914	;	Hahn	;	H.	;	Locally connected continuum is a continuous image of [0,1].
1914	;	Mazurkiewicz	;	S.	;	Sierpinski carpet contains only ramification points of infinite order.
1915	;	Sierpinski	;	W.	;	Half homogeneous Sierpinski carpet containing a copy of every planar curve.
1915	;	Sierpinski	;	W.	;	Sierpinski triangle with only ramification points.
1916	;	Moore	;	R.L.	;	Chainable continuum.
1918	;	Sierpinski	;	W.	;	Any continuum is sigma connected, not a countable union of disjoint closed sets.
1918	;	Janiszewski	;	Z.	;	Foundation of Fundamenta Mathematicae journal (with W. Sierpinski and S. Mazurkiewicz). 
1920	;	Antoine	;	L. 	;	Antoine's necklace (wild embedding of the Cantor set).
1920	;	Mazurkiewicz	;	S.	;	Locally connected continuum is a continuous image of [0,1].
1920	;	Moore	;	R.L.	;	Two non-cut points in any continuum.
1922	;	Antoine	;	L. 	;	Antoine's arc (wild embedding of the arc).
1922	;	Knaster	;	B.	;	Buckethandle in a round shape.
1922	;	Knaster	;	B.	;	Pseudo-arc, the nondegenerate hereditarily indecomposable continuum.
1923	;	Wazewski	;	T.	;	Wazewski universal dendrite containing a copy of any dendrite.
1924	;	Alexander	;	J.W.	;	Alexander horned sphere, a wild embedding of a sphere into space.
1924	;	Mazurkiewicz	;	S.	;	Each locally connected homogeneous plane continuum is a simple closed curve.
1925	;	Gehman	;	H.M.	;	Dendrite with ramification points of order 3 and end points forming the Cantor set.
1926	;	Menger	;	K.	;	Homogeneous Menger sponge containing a copy of every curve.
1927	;	Kuratowski	;	K.	;	A point of irreducibility in a continuum is not contained in two proper subcontinua (a characterization).
1927	;	Vietoris	;	L.	;	Solenoid (in a sequence folding tube in a previous tube twice).
1929	;	Roberts	;	J.H.	;	Upper semicontinuous decomposition of the plane into nonseparating locally connected subcontinua.
1930	;	Mazurkiewicz	;	S.	;	A typical continuum is hereditarily indecomposable.
1930	;	Dantzig	;	D. von	;	Homogeneity of a solenoid.
1930	;	Kurtowski	;	K.	;	Planability test for local dendrites (cannot contain two special continua).
1930	;	Whyburn	;	G.T.	;	Whyburn's curve, a continuum every subcontinuum of which separates the plane.
1931	;	Keller	;	O.H.	;	Hilbert cube is homogeneous.
1932	;	Miller	;	E.W.	;	A dendrite not containing its proper copy.
1932	;	Waraszkiewicz	;	Z.	;	Waraszkiewicz's spirals ( an uncountable family of continuously incomparable planar curves).
1934	;	Borsuk	;	K.	;	The dunce hat (Borsuk's tube, acyclic polyhedron which is not the union of two acyclic polyhedra).
1935	;	Mazurkiewicz	;	S. 	;	Any compact metric space of dimension 2 contains a nondegenerate indecomposable continuum.
1936	;	Whyburn	;	G.T.	;	Decomposition of 3-space into 3-space using Antoine's arc and points.
1937	;	Sierpinski	;	W.	;	Arc mapped onto Hilbert cube. 
1937	;	Freudenthal	;	H.	;	Solenoid as an inverse limit.
1937	;	Claytor	;	S.	;	Two Claytor continua block planarity of a Peano continuum.  
1944	;	Sorgenfrey	;	R.H.	;	Every nondegenerate unicoherent continuum which is not a triod is irreducible.
1945	;	Besicovitch	;	A.S.	;	A dendrite such that no two of its open sets are homeomorphic.
1947	;	Borsuk	;	K.	;	An example of a simple arc in space whose projection in every plane has interior points.
1948	;	Bing 	;	R.H.	;	Homogeneity of the pseudo-arc.
1948	;	Moise	;	E.E.	;	Indecomposable planar continuum homeomorphic to each of its nondegenerate subcontinua (the pseudo-arc).
1948	;	Jones	;	F. B.	;	T function (the complement of T(A) contains the interior points of subcontinua not meeting A).
1951	;	Hamilton	;	O.H.	;	Each chainable continuum has the fixed-point property.
1951	;	Bing	;	R.H.	;	Planar non-chainable circularly chainable hereditarily indecomposable continuum (a pseudo-circle).
1952	;	Anderson	;	R.D.	;	A continuous decomposition of the plane into nonseparating subcontinua.
1958	;	Anderson	;	R.D.	;	Menger universal curve is homogeneous.
1959	;	Anderson	;	R.D.	;	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1959	;	Choquet	;	G.	;	A plane continuum no two of whose nendegenerate subcontinua are homeomorphic.
1959	;	Isbell	;	J.R.	;	Chainable continuum is an inverse limit of an inverse sequence of arcs.
1959	;	Bing 	;	R.H.	;	The circle of pseudo-arcs.
1959	;	Jones	;	F. B.	;	The circle of pseudo-arcs.
1961	;	Lelek	;	A.	;	The Lelek fan (a smooth fan with a dense set of endpoints).
1962	;	Lelek	;	A.	;	Weakly chainable continua are exactly continuous images of the pseudo-arc.
1963	;	Borsuk 	;	K.	;	Borsuk nonplanar fan.
1964	;	Henderson	;	G.	;	Arc is the only decomposable hereditarily equivalent continuum.
1964	;	Lelek	;	A.	;	Span zero (no two points can change the position on a continuum).
1964	;	Henderson	;	G.	;	The pseudo-arc is an inverse limit using only one binding map.
1964	;	Charatonik	;	J.J.	;	Unicoherence of locally connected continua is an invariant under confluent mappings.
1965	;	Effros	;	E.G.	;	The group of homeomorphisms acts locally.
1965	;	Schori	;	R.M.	;	Universal chainable continuum.
1967	;	Smale	;	S. 	;	Buckethandle in a horseshoe shape as the fixed set of a mapping square into a horseshoe.
1967	;	Cook	;	H.	;	Cook's continuum (a continuum admitting only the identity or a constant mapping onto itself).
1969	;	Krasinkiewicz	;	J.	;	Sierpinski universal plane curve is 1/2-homogeneous.
1970	;	Rogers	;	J.T.	;	A pseudo-solenoid  is a common model for circle-like continua.
1970	;	Rogers	;	J.T.	;	The pseudo-circle is not homogeneous.
1970	;	Fearnley	;	L.	;	The pseudo-circle is unique.
1971	;	Lelek	;	A.	;	Houston problem book.
1972	;	Ingram	;	W.T.	;	An atriodic tree-like continuum with positive span.
1972	;	Bennett	;	R.B.	;	Menger universal curve is countable dense homogeneous.
1972	;	Charatonik	;	J.J.	;	Problem posing (?) challenge over problem solving (exists) and generalisations (for all).
1973	;	Nadler	;	Sam B. Jr.	;	The indecomposability of the dyadic solenoid.
1974	;	Rosenholtz	;	I.	;	Open image of a chainable continuum is chainable.
1975	;	Ungar	;	G.S.	;	2-homogeneous continuum is locally connected.
1977	;	Hagopian	;	Ch.L.	;	Solenoids (homogeneous continua with only arc subcontinua).
1977	;	Rogers	;	J.T.	;	Solenoids of pseudo-arcs.
1978	;	Charatonik	;	J.J.	;	Arc-like openly homogenous continuum is the pseudo-arc.
1978	;	Curtis	;	D.W.	;	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1978	;	Schori	;	R.M.	;	Hyperspaces of closed subsets of Peano continua are Hilbert cubes.
1978	;	Illanes	;	A.	;	Hyperspaces of sets. Book I 
1978	;	Grispolakis	;	J.	;	Universal smooth dendroid.
1978	;	Tymchatyn	;	E.D.	;	Universal smooth dendroid.
1979	;	Bellamy	;	D.P.	;	A nonplanar tree-like continuum which admits a fixed point free mapping.
1979	;	Ingram	;	W.T.	;	Hereditarily indecomposable tree-like continua.
1980	;       Krasinkiewicz   ;	J.	;       A dendroid with a monotone open map onto an arc.
1980	;       Minc	;       P.	;       A dendroid with a monotone open map onto an arc.
1980	;	Oversteegen	;	Lex G.	;	A dendroid with a monotone open map onto an arc.
1980	;	Mill	;	J. van	;	A Peano continuum homeomorphic to its own square but not to its countable infinite product.
1980	;	Iliadis	;	S.D.	;	Universal completely regular continuum (each nondegenerate subcontinuum has a nonempty interior).
1982	;	Oversteegen	;	Lex	;	Indecomposable homogeneous planar continuum has span zero.
1982	;	Tymchatyn	;	E.D.	;	Indecomposable homogeneous planar continuum has span zero.
1984	;	Charatonik	;	J.J.	;	Example of a smooth dendroid without ordinary points.
1984	;	Nikiel	;	J.	;	Gehman dendroid is the only dendrite with its set of end-points homeomorphic to the Cantor set.
1985	;	Mackowiak	;	T.	;	A universal hereditarily indecomposable continuum.
1986	;	Kennedy	;	J.	;	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1986	;	Rogers	;	J.T.	;	Pseudo-circle has uncountably many orbits each of which is the union of uncountably many composants.
1988	;	Mackowiak	;	T.	;	A characterization of finitely irreducible continua.
1989	;	Charatonik	;	J.J.	;	A fan is smooth iff can be embedded into the Cantor fan.
1989	;	Charatonik	;	W.J.	;	A fan is smooth iff can be embedded into the Cantor fan.
1989	;	Charatonik	;	W.J.	;	Lelek fan is the unique smooth fan with a dense set of endpoints.
1990	;	Kuperberg	;	K.	;	A locally connected homogeneous non-bihomogeneous continuum of dimension 7.
1990	;	Krupski	;	P.	;	Homogeneous tree-like continua are hereditarily indecomposable.
1990	;	Prajs	;	J.R.	;	Homogeneous tree-like continua are hereditarily indecomposable.
1991	;	Minc	;	P.	;	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1991	;	Transue	;	W.R.R.	;	A transitive map on [0,1] whose inverse limit is the pseudo-arc.
1992	;	Nadler	;	Sam B. Jr.	;	Continuum Theory. An Introduction. Book II
1993	;	Nadler	;	Sam B. Jr.	;	A continuum separated by each of its nondegenerate proper subcontinua.
1993	;	Seldomridge	;	Gary A.	;	A continuum separated by each of its nondegenerate proper subcontinua.
1993	;	Bellamy	;	D.	;	A tree-like continuum without the fixed-point property.
1993	;	Minc	;	P.	;	An atriodic simple-4-od-like continuum which is not simple-triod-like.
1993	;	Aarts	;	J.M.	;	Hairy arc.
1993	;	Oversteegen	;	L.G.	;	Hairy arc.
1994	;	Bandt	;	Ch.	;	Non-zero composants of the Buckethandle are homeomorphic.
1995	;	Kennedy	;	J.	;	Buckethandle as an inverse limit of circles using a single bonding map.
1996	;	Hagopian	;	Ch. L.	;	Simply connected plane continua have the fixed-point property.
1999	;	Lewis	;	W.	;	An example of a chainable continuum that admits an exactly 2-to-1 mapping onto a continuum.
1999	;	Illanes	;	A.	;	Hyperspaces. Book III
1999	;	Nadler	;	Sam B. Jr.	;	Hyperspaces. Book III
1999	;	Lewis	;	W.	;	Pseudo-arc maturity.
1999	;	Illanes	;	A.	;	The Continuum theory hyperspace in Mexico.
1999	;	Minc	;	P.	;	There exists a tree-like weakly chainable continuum without the fixed-point property.
2000	;	Prajs	;	J.R.	;	A continuous decomposition of the Menger curve into pseudo-arcs.
2002	;	Illanes	;	A.	;	Buckethandle admits no mean.
2003	;	Minc	;	P.	;	Buckethandle is mapped onto a planar dedroid with point-inverses at most of cardinality 3.
2003	;	Minc	;	P.	;	Planar dendroid contains a single point bottleneck.
2005	;	Macias	;	S.	;	Topics on continua. Book IV
2010	;	Illanes	;	A.	;	The arc is the only chainable continuum admitting a mean.
2010	;	Villanueva	;	H.	;	The arc is the only chainable continuum admitting a mean.
2011	;	Hoehn	;	L.C.	;	A non-chainable plane continuum with span zero.
2012	;	Ingram	;	W.T.	;	Inverse limit of books on inverse limit...
2013	;	Vejnar	;	B.	;	Acrless-arc, the arc-like arc-less continuum with two endpoints.
2013	;	Hoehn	;	L.C.	;	An uncountable collection of copies of a non-chainable tree-like continuum in the plane.
2014	;	Sturm	;	F. 	;	Pseudo-solenoid is not continuously homogeneous.
2015	;	Mill	;	J. van	;	Pseudo-arc is the only continuum with homeomorphically near property.
2015	;	Banic	;	I.	;	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
2015	;	Martinez-de-la-Vega	;	V.	;	Standard universal dendrite of order 3 as an inverse limit of arcs with one binding map.
2016	;	Prajs	;	J.R.	;	Arcwise connected homogeneous continuum is a continuous image of the Cantor fan.
2016	;	Hoehn	;	L.C.	;	Classification of planar homogeneous continua.
2016	;	Oversteegen	;	Lex	;	Classification of planar homogeneous continua.
2016	;	Vejnar	;	B.	;	Two non-block points in any continuum.
2020	;	Hoehn	;	L.C.	;	Classification of hereditarily equivalent plane continua.
2020	;	Oversteegen	;	Lex	;	Classification of hereditarily equivalent plane continua.