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The relationship between a fuzzy uniformity and its family of \(\alpha\)-level uniformities. (English) Zbl 0871.54009
Summary: We show that a fuzzy uniformity \({\mathcal D}\) is uniquely determined by its family of \(\alpha\)-level uniformities \(({\mathcal D}^\alpha: \alpha\in (0,1))\). On the other hand, if a family \(({\mathbf D} (\alpha): \alpha\in (0,1))\) of uniformities on a set \(X\) is given and the family satisfies certain conditions, then there exists a unique fuzzy uniformity \({\mathcal D}\) on \(X\) whose family of \(\alpha\)-level uniformities is the given family.

MSC:
54A40 Fuzzy topology
03E72 Theory of fuzzy sets, etc.
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