Compact Hausdorff fuzzy topological spaces are topological |
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Authors: | R Lowen |
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Institution: | Department of Mathematics, Vrije Universiteit Brussel, Brussel 1050, Belgium |
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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. |
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Keywords: | 54A40 54A05 03E72 54C08 |
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