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Let a continuum be locally connected and let . By a
*cyclic element* of containing we mean either the singleton
if is a cut point or an end point of , or the set consisting of
and of all points such that no point of cuts between
and , otherwise (see e.g. [Whyburn 1942, Chapter 4, §2, p. 66]).

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

*2001-11-30*