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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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##### References:
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