Geodesic
On convergence in the space of closed subsets of a metric space
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 3, pp. 565-570 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the space ${\rm clos}(X)$ of closed subsets of unbounded (not necessarily separable) metric space $(X, \varrho_{_X})$ endowed with the metric $\rho_{_X}^{\rm cl}$ 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 $(X, \varrho_{_X})$ is totaly bounded, then convergence in the space $\left({\rm clos}(X), \rho_{_X}^{\rm cl}\right)$ of a sequence $\{F_i\}_{i=1}^\infty$ to $F$ is equivalent to convergence in the sense of Wijsman, that is to convergence for each $x \in X$ of the distances $\varrho_{_X}(x, F_i)$ to $\varrho_{_X}(x, F).$
Keywords: space of closed subsets of a metric space, metrizability.
Mots-clés : Wijsman convergence 
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     title = {On convergence in the space of closed subsets of a metric space},
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E. A. Panasenko. On convergence in the space of closed subsets of a metric space. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 3, pp. 565-570. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_3_a8/

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