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By an arc-structure on an arbitrary space
we
understand a function
such that for every two
distinct points
and
in
the set
is an arc from
to
and that the following metric-like axioms are satisfied for every points
,
and
in
:
- (1)
-
;
- (2)
-
;
- (3)
-
,
with equality prevailing whenever
.
We put
to denote that the space
is equipped with
an arc-structure
(see [Fugate et al. 1981, p. 546]). Note
that if there exists an arc-structure on a continuum, then
the continuum is arcwise connected.
Next: atomic
Up: Definitions
Previous: arc-smooth
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30