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Displaying similar documents to “On the product of probabilistic metric spaces”

Coincidence of Vietoris and Wijsman Topologies: A New Proof

Holá, L’. (1997)

Serdica Mathematical Journal

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Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies...

On natural metrics.

Claudi Alsina, Enric Trillas (1977)

Stochastica

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In the present note we study the effective construction of a natural generalized metric structure (on a set), obtaining as particular case the result of Menger. In the case of groups, we analyze its topology and its structure of natural proximity space (in the sense of Efremovic).