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converge 0-regularly

A sequence of sets \{A_n\}$ contained in a metric space X$ with a metric d$ is said to converge 0-regularly to its limit A
= \mathrm{Lim}\,A_n$ (see hyperspace ) provided that for each \varepsilon > 0$ there is a \delta>0$ and there is an index n_0 \in \mathbb{N}$ such that if n > n_0$ then for every two points p, q \in A_n$ with d(p,q) < \delta$ there is a connected set C_n \subset A_n$ satisfying conditions p, q \in C_n$ and diam_n <
\varepsilon $ (see [Whyburn 1942, Chapter 9, §3, p. 174]).
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Next: convex Up: Definitions Previous: converges homeomorphically to the
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30