Separation axioms for completeness and total boundedness in fuzzy pseudo metric spaces
type: Item
instance of: scholarly article
title: Separation axioms for completeness and total boundedness in fuzzy pseudo metric spaces
zbMATH Open document ID: 0589.54006
DOI: 10.1016/0022-247X(85)90281-1
author: Zi Ke Deng
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The paper mainly aims at the introduction of fuzzy pseudo-metric on a set X along with the pseudo-metric topology and continues the author's study in ibid. 86, 74-95 (1982; Zbl 0501.54003). For discussing the properties of the topology, the author introduces topological properties like separation axioms, separability, axioms of countability and a compactness-like concept which the author calls m-compactness. A fuzzy metric on X, Cauchy sequences, m-convergence and subsequently completeness along with total boundedness are also introduced. For Urysohn's lemma the author uses the fuzzy unit interval with some variation of its previous version. The expected relations between the separation axioms are valid. The equivalence of separability and 2nd countability in a fuzzy pseudo-metric space is established. The most interesting result is a version of Baire's theorem and the equivalence of m-compactness with total boundedness and completeness. The author also introduces contraction mappings along with a fixed-point theorem.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 3947149
zbMATH Keywords: fuzzy unit interval
zbMATH Keywords: separability
zbMATH Keywords: 2nd countability
zbMATH Keywords: fuzzy pseudo-metric space
zbMATH Keywords: Baire's theorem
zbMATH Keywords: m-compactness
zbMATH Keywords: total boundedness
zbMATH Keywords: completeness
reviewed by: Sobhakar Ganguly
MaRDI profile type: Publication
cites work: Normality in fuzzy topological spaces
cites work: Fuzzy pseudo-metric spaces
cites work: Metric spaces in fuzzy set theory
cites work: Q5728102
description: scientific article; zbMATH DE number 3947149