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Given a continuum
with an arc-structure
, a subset
of
is said to be convex provided that for each pair of
points
and
of
the arc
is a subset of
. If
is a convex
subcontinuum of
, then
is an arc-structure on
. We
define
to be locally convex at a point
provided that
for
each open set
containing
there is a convex set
such that
(see [Fugate et al. 1981, I.2, p. 548-549]).
Next: continuum
Up: Definitions
Previous: converge 0-regularly
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30