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aposyndetic

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 p \in X$ and for each q \in X \setminus \{p\}$ there exists a subcontinuum K$ of X$ and an open set U$ of X$ such that p \in U \subset K \subset X \setminus \{q\}$ (see e.g.[Nadler 1992, Exercise 1.22, p. 12]).
next up previous contents index
Next: arc Up: Definitions Previous: almost chainable
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30