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Compact Hausdorff fuzzy topological spaces are topological

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
12
Issue
1
Identifiers
DOI: 10.1016/0166-8641(81)90030-4
Disciplines
  • Mathematics

Abstract

Abstract Many examples of compact fuzzy topological spaces which are highly non topological are known [5, 6]. Equally many examples of Hausdorff fuzzy topological spaces which are highly non topological can be given. In this paper we show that the two properties - compact and Hausdorff - combined however necessarily imply that the fuzzy topological space is topological. This at once solves some open questions with regard to the compactification of fuzzy topological spaces [8]. It also emphasizes once more the particular role played by compact Hausdorff topological spaces not only in the category of topological spaces but even in the category of fuzzy topological spaces.

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