## Completeness using pairs of filters.(English)Zbl 0770.54027

The authors investigate three kinds of completeness in quasi-uniform $$T_ 1$$-spaces: $$D$$-completeness, strong $$D$$-completeness, and pair completeness (=bicompleteness). In particular these properties are studied in the class of uniformly regular quasi-uniform spaces.
Among other things they show that those three concepts of completeness agree in a uniform space or in any equinormal uniformly regular quasi- uniform space.
Reviewer: H.P.Künzi (Bern)

### MSC:

 5.4e+16 Uniform structures and generalizations 5.4e+53 Baire category, Baire spaces
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### References:

 [1] Császár, Á., Extensions of quasi-uniformities, Acta. Math. Hungar., 37, 121-145 (1981) · Zbl 0431.54012 [2] Doitchinov, D., On completeness of quasi-uniform spaces, C.R. Acad. Bulgare Sci., 41, 7, 5-8 (1988) · Zbl 0649.54015 [3] Doitchinov, D., On completeness in quasi-metric spaces, Topology Appl., 30, 127-148 (1988) · Zbl 0668.54019 [4] Doitchinov, D., A concept of completeness of quasi-uniform spaces, Topology Appl., 38, 205-217 (1991) · Zbl 0723.54030 [5] Fletcher, P.; Hunsaker, W., Uniformly regular quasi-uniformities, Topology Appl., 37, 285-291 (1990) · Zbl 0707.54021 [6] Fletcher, P.; Lindgren, W. F., Quasi-Uniform Spaces (1982), Marcel Dekker: Marcel Dekker New York · Zbl 0402.54024 [7] Fletcher, P.; Lindgren, W. F., Compactifications of totally bounded quasi-uniform spaces, Glasgow Math. J., 28, 31-36 (1986) · Zbl 0583.54017 [10] Lindgren, W. F.; Fletcher, P., A construction of the pair completion of a quasi-uniform space, Canad. Math. Bull., 21, 53-58 (1978) · Zbl 0393.54019 [11] Lindgren, W. F.; Fletcher, P., Equinormal quasi-uniformities and quasi-metrics, Glas. Mat. Ser. III, 13, 33, 111-125 (1978) · Zbl 0381.54017
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