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Given a continuum X with an arc-structure A, a subset
Z of X is said to be convex provided that for each pair of
points
x and y of Z the arc A(x,y) is a subset of Z. If Z is a convex
subcontinuum of X, then A|Z x Z is an arc-structure on Z. We
define X to be locally convex at a point
provided that
for
each open set U containing p there is a convex set Z such that
(see [42, I.2, p. 548-549]).
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-02-21