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The statement that the sequence
*converges homeomorphically to the continuum* means there
exists a sequence
of homeomorphisms such
that, for each positive integer , is a
homeomorphism from onto and for each positive
number
there exists a positive integer such
that if then, for all , dist
.

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*Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih*

*2001-11-30*