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A connected space X is aposyndetic at H with respect
to K if there is a closed connected subset of X with H
in its interior and not intersecting K, and X is
aposyndetic if it is aposyndetic at each point with respect
to every other point.
A continuum X is said to be aposyndetic provided that for
each point
and for each
there exists a
subcontinuum K of X and an open set U of X such that
(see e.g.[65, Exercise 1.22, p. 12]).
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-02-21