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A sequence of sets contained in a metric space
with a metric is said to *converge 0-regularly* to its limit
(see hyperspace ) provided that for each
there is a
and there is an index
such that if then for
every two points
with
there is a connected
set
satisfying conditions
and
(see [Whyburn 1942, Chapter 9, §3, p. 174]).

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

*2001-11-30*