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ON CONVERGENCE IN THE SPACE OF CLOSED SUBSETS OF A METRIC SPACE

Annotation

We consider the space closX of closed subsets of unbounded (not necessarily separable) metric space X, ϱ X endowed with the metric ρ X cl introduced in [ Zhukovskiy E.S., Panasenko E.A. // Fixed Point Theory and Applications. 2013:10]. It is shown that if any closed ball in the space X, ϱ X is totaly bounded, then convergence in the space clos X , ρ X cl of a sequence F i i=1 ∞ to F is equivalent to convergence in the sense of Wijsman, that is to convergence for each x∈X of the distances ϱ X x, F i to ϱ X x, F .

Keywords

space of closed subsets of a metric space; Wijsman convergence; metrizability

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DOI

10.20310/1810-0198-2017-22-3-565-570

UDC

515.124

Pages

565-570

Received

2017-02-15

Section of issue

Functional-differential equations and inclusions and their applications to mathematical modeling

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