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Covering by discrete and closed discrete sets

By Santi Spadaro

Abstract

AbstractSay that a cardinal number κ is small relative to the space X if κ<Δ(X), where Δ(X) is the least cardinality of a non-empty open set in X. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire σ-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces

Publisher: Elsevier B.V.
Year: 2009
DOI identifier: 10.1016/j.topol.2008.09.009
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