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

DOI: 10.2140/pjm.1978.79.37

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|≦ 2^χ(X)wL(X). Examples are given of a nonregular Hausdorff space Z such that |Z| > 2^χ(Z)wL(Z) and a zero-dimensional Hausdorff space Y such that |Y | > 2^{ψ(Y )∂(Y )wL(Y )}. Define rψ(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) ≦ rψ(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