Topology Proceedings 28 No. 2 (2004), pp. 445-465

Elimination of covers in completeness

Szymon Dolecki

It is shown that nonadherent filters can totally eliminate covers from topological arguments, which enhances the unity of convergence approach. In particular, cocomplete collections of nonadherent filters replace complete collections of covers. Arhangel'skii-Frolík characterization of Cech complete spaces and its generalizations by Frolík are extended and refined. Hereditary completeness is dually characterized (in terms of pavements of the upper Kuratowski convergence). As a corollary a characterization by Dolecki and Mynard of the pretopologicity of the upper Kuratowski convergence (which generalizes to arbitrary convergences the characterization of Hofmann and Lawson) is recovered.

Keywords: Cech completeness

Mathematics Subject Classification: 54A20 54D99

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Topology Proceedings, Volume 28, No. 2 (2004)
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