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converges homeomorphically to the continuum

The statement that the sequence M_1, M_2, \cdots$ converges homeomorphically to the continuum M$ means there exists a sequence h_1, h_2, \cdots$ of homeomorphisms such that, for each positive integer i$, h_i$ is a homeomorphism from M_i$ onto M$ and for each positive number \varepsilon$ there exists a positive integer N$ such that if j > N$ then, for all x$, dist (h_j(x),x) <
\varepsilon$.
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Next: converge 0-regularly Up: Definitions Previous: continuous selection of
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30