Covering by discrete and closed discrete sets

Santi Domenico Spadaro, Santi Spadaro

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1 Citation (Scopus)

Abstract

Say that a cardinal number k is emph{small} relative to the space X if k is smaller than 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.
Original languageEnglish
Pages (from-to)721-727
Number of pages7
JournalTopology and its Applications
Volume156
Publication statusPublished - 2009

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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