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A topological space is said to be
*-connected* provided that is not the union of
more than one and at most countably many nonempty, mutually
disjoint, closed subsets.
A continuum is *-connected* if each two of its
points can be connected by an hereditarily decomposable
irreducible subcontinuum.

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

*2001-11-30*