The N-compactness in L-fuzzy topological spaces
type: Item
instance of: scholarly article
title: The N-compactness in L-fuzzy topological spaces
zbMATH Open document ID: 0639.54006
DOI: 10.1016/0022-247X(87)90214-9
author: Dongsheng Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: While the problem of defining compactness in fuzzy topological spaces would seem trivial, the formal generalization has many deficiencies. For example, there is no Tikhonov theorem and a one point set need not be fuzzy compact. Even the widely used fuzzy compactness of Lowen and the strong fuzzy compactness of Gantner, Steinlage, and Warren are not necessarily inherited by fuzzy closed subsets. \textit{Guojun Wang} [J. Math. Anal. Appl. 94, 1-23 (1983; Zbl 0512.54006)] introduced N- compactness to overcome this problem and showed it equivalent to fuzzy and strong fuzzy compactness under a \(T_ 2\)-like separation axiom. The present paper extends Wang's work from [0,1] to arbitrary L-fuzzy topological spaces and gives a ``geometrical'' characterization of N- compactness.
reviewed by: Louis M. Friedler
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 4042802
zbMATH Keywords: fuzzy compactness
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042802