Vol. 100, No. 2, 1982

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Collections of covers of metric spaces

Ted R. Pettis

Vol. 100 (1982), No. 2, 425–435
Abstract

In this paper cardinality κ collections of open covers of a topological space satisfying various conditions are studied. When κ = ω some of the conditions are equivalent to the space being metrizable and the union of a compact set and a discrete set. For a metrizable space some of the conditions are equivalent to complete metrizability. If κω then the relationship between some of the conditions and the existence of scales is examined.

Mathematical Subject Classification 2000
Primary: 54E30
Secondary: 54E18
Milestones
Received: 3 September 1980
Revised: 15 December 1980
Published: 1 June 1982
Authors
Ted R. Pettis