Covering by Discrete and Closed Discrete Sets
نویسنده
چکیده
Say that a cardinal number κ is small relative to the space X if κ < ∆(X), where ∆(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.
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