Ingram's Atriodic Continuum

INGRAM COMMENT (modified):

Figure A represents the first and second composite of a mapping f of a triod $T = OA \cup OB \cup OC$, onto itself. The mapping f has the property that f(O) = B, f(A) = C, f(B)= C, f(C) = C, f(C/2) = O, f(B/3) =O, f(B/2) = A/2, f(2B/3)= O, f(A/4)= O, f(A/2) = A, f(3A/4) = O and the mapping is piecewise linear. In the picture, the black square represents O, the green arm is the image of OA, the blue arm is the image of OB and the red arm is the image of OC. The inverse limit of the inverse sequence, T,f, is an atriodic tree-like continuum which is not chainable [Fund. Math., 77(1972), 99 - 107]. We call it an Ingram's Atriodic Continuum.

If one imagines that the fat triod in the top of the Fgure A represents the first of a sequence of tree chains covering the inverse limit then the blue-green-red folded triod represents the next terms of the sequence of covers.

Figure ( A ) First steps in the construction of the Ingram's Atriodic Continuum


Figure ( B ) Next step in the construction of the Ingram's Atriodic Continuum


Source files: a.cdr . a.eps . a.gif . a.mws . a.txt . b.cdr . b.gif . b.mws . b.txt . latex.tex . title.txt .

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