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uniformly continuum-chainable

A continuum X$ is said to be uniformly continuum-chainable if for each positive number \varepsilon$ there is an integer k=k(\varepsilon)$ such that for each pair x$,y$ of points of X$, there are subcontinua A_1, \cdots, A_k$ of X$ each of diameter less than \varepsilon$ such that x\in A_1$, y\in A_k$ and A_i \cap A_j \ne \emptyset$ whenewer \vert i-j\vert \leq 1$.
next up previous contents index
Next: uniquely arcwise connected Up: Definitions Previous: unicoherent
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30