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doi:10.1016/0166-8641(81)90030-4 
Copyright © 1981 Published by Elsevier Science B.V. All rights reserved.
Compact Hausdorff fuzzy topological spaces are topological
Received 27 June 1979;
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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.
Mathematical subject codes: 54A40; 54A05, 03E72, 54C08
