Vol. 79, No. 1, 1978

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ISSN: 0030-8730
Cardinal inequalities for topological spaces involving the weak Lindelof number

Murray Bell, John Norman Ginsburg and R. Grant Woods

Vol. 79 (1978), No. 1, 37–45
Abstract

Let wL(X), χ(X), ψ(X), c(X), and (X) denote respectively the weak Lindelof number, character pseudocharacter, cellularity, and tightness of a Hausdorff topological space X. It is proved that if X is a normal Hausdorff space then |X|2χ(X)wL(X). Examples are given of a nonregular Hausdorff space Z such that |Z| > 2χ(Z)wL(Z) and a zero-dimensional Hausdorff space Y such that |Y | > 2ψ(Y )(Y )wL(Y ). Define (X) = min{κ : each closed subset of X is the intersection of the closures of κ of its neighborhoods}. It is proved that c(X) (X)wL(X). Related open questions are posed.

Mathematical Subject Classification 2000
Primary: 54A25
Milestones
Received: 3 March 1978
Revised: 19 April 1978
Published: 1 November 1978
Authors
Murray Bell
John Norman Ginsburg
R. Grant Woods