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.
Lingua originale | English |
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pagine (da-a) | 721-727 |
Numero di pagine | 7 |
Rivista | Topology and its Applications |
Volume | 156 |
Stato di pubblicazione | Published - 2009 |
All Science Journal Classification (ASJC) codes
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