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Fuzzy proximities compatible with Lowen fuzzy uniformities. (English) Zbl 0612.54006

The authors introduce a definition of fuzzy proximity appropriate for Lowen fuzzy uniformities [R. Lowen, J. Math. Anal. Appl. 82, 370- 385 (1981; Zbl 0494.54005)]. Every Lowen uniformity generates a fuzzy proximity, which induces the same fuzzy topology as the uniformity. Every classical proximity also generates a fuzzy proximity; in this case the induced fuzzy topology is topologically generated from the topology of the original proximity. The paper concludes with examples and remarks comparing Hutton and Lowen uniformities as well as proximity definitions, including one proposed earlier by A. K. Katsaras and the authors [J. Math. Anal. Appl. 99, 320-337 (1984; Zbl 0558.54002)].
Reviewer: A.J.Klein

MSC:

54A40 Fuzzy topology
54E05 Proximity structures and generalizations
54E15 Uniform structures and generalizations
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References:

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