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unicoherent

A connected topological space S$ is said to be unicoherent provided that whenever A$ and B$ are closed, connected subsets of S$ such that S=A\cup B$, then A\cap B$ is connected. Let a continuum X$ and its subcontinuum Y$ be given. Then X$ is said to be unicoherent at Y$ provided that for each pair of proper subcontinua A$ and B$ of X$ such that X = A \cup B$ the intersection A \cap B \cap Y$ is connected (see [Owens 1986, p. 146]).
next up previous contents index
Next: uniformly continuum-chainable Up: Definitions Previous: triod
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30