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Zbl 0612.54006
Artico, Giuliano; Moresco, Roberto
Fuzzy proximities compatible with Lowen fuzzy uniformities. (English)
[J] Fuzzy Sets Syst. 21, 85-98 (1987). ISSN 0165-0114

The authors introduce a definition of fuzzy proximity appropriate for Lowen fuzzy uniformities [{\it 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 {\it A. K. Katsaras} and the authors [J. Math. Anal. Appl. 99, 320-337 (1984; Zbl 0558.54002)].
[A.J.Klein]

MSC 2000:: *54A40 Fuzzy topology
54E05 Proximity structures and generalizations
54E15 Uniform structures and generalizations

Keywords: fuzzy proximity; Lowen fuzzy uniformities; Hutton and Lowen uniformities

Citations: Zbl 0494.54005; Zbl 0558.54002

Cited in: Zbl 1005.54011 Zbl 0983.54009 Zbl 0917.54009 Zbl 0827.54003 Zbl 0797.54021 Zbl 0758.54002 Zbl 0689.54003

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