Cardinal inequalities for topological spaces involving the weak Lindelof number

Abstract

Let wL(X), (X), f(X), e(X) It is proved that if X is a normal Hausdorff space then \X\ 2%U)WLU) Examples are given of a nonregular Hausdorff space Z such that \Z\ > 2 x(z)u7lrCZ) and a zero-dimensional Hausdorff space Y such that | Y\ >2^ )dmwUY \ Define rf(X)= min {fc: each closed subset of X is the intersection of the closures of K of its neighborhoods}. It is proved that c(X) rf(X)wL(X). Related open questions are posed. 1 Introduction* Let X be a Hausdorff topological space. The