Uniformly regular quasi-uniformities. (English) Zbl 0707.54021

Fletcher, P.; Hunsaker, W.

Topology Appl. 37, No. 3, 285-291 (1990).

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.)

Keywords:

completeness; orthocompactness; semistratifiability; uniform regularity; quiet quasi-uniform space; point symmetric uniformly regular quasi- uniform space; Lebesgue quasi-uniformity; compact quasi-uniformity; continuous quasi-metric; Michael line

Citations:

Zbl 0649.54015

References:

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