The Wijsman topology of a fuzzy metric space

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 2016 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 300, pages 57-71 (issn: 0165-0114,

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Authors: Javier Gutiérrez García; Jesús Rodríguez-López; Salvador Romaguera; Manuel Sanchis;

doi: 10.1016/j.fss.2015.08.005

The Wijsman topology of a fuzzy metric space

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Abstract

[EN] We introduce and study the notions of lower Wijsman topology, upper Wijsman topology and Wijsman topology of a fuzzy metric space in the sense of Kramosil and Michalek. In particular, quasi-uniformizability, uniformizability, quasi-metrizability and metrizability of these topologies are discussed. Their relations with other hypertopologies are also analyzed. Corresponding results to the Wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric.

J. Gutierrez Garcia acknowledges the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-02. J. Rodriguez-Lopez, S. Romaguera and M. Sanchis also acknowledge the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.

Related Organizations

Universitat Politècnica de València
Spain
Jaume I University
Spain
University of the Basque Country
Spain

Keywords

Fuzzy topology, (Quasi-)metrizable, Fuzzy metric space, Vietoris topology, Separability of topological spaces, Hausdorff fuzzy metric, Separable, Wijsman topology, The Hausdorff fuzzy metric, (quasi-)metrizable space, Second countable, Lower separation axioms (\(T_0\)--\(T_3\), etc.), second countable space, Metric spaces, metrizability, Bispace, Hyperspaces in general topology, fuzzy metric space, bispace, separable space, MATEMATICA APLICADA

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