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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]).

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*Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih*

*2001-11-30*