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Uniformly regular quasi-uniformities. (English) Zbl 0707.54021

Summary: The concept of uniform regularity is studied. Every quiet quasi-uniform space is uniformly regular, and every point symmetric uniformly regular quasi-uniform space that is complete (in the sense of D. Doichinov [C.R. Acad. Bulg. Sci. 41, No.7, 5-8 (1988; Zbl 0649.54015)] is quiet. Every Lebesgue quasi-uniformity (in particular every compact quasi- uniformity) that is uniformly regular is quiet. Every continuous quasi- metric is uniformly regular, but the Michael line has a continuous quasi- metric that is not quiet.

MSC:

54E15 Uniform structures and generalizations
54E20 Stratifiable spaces, cosmic spaces, etc.
54E52 Baire category, Baire spaces
54D30 Compactness
54E05 Proximity structures and generalizations
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

Citations:

Zbl 0649.54015
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Full Text: DOI

References:

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