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.

SPADARO, S.D. (2009). Covering by discrete and closed discrete sets. TOPOLOGY AND ITS APPLICATIONS, 156(4), 721-727 [10.1016/j.topol.2008.09.009].

Covering by discrete and closed discrete sets

SPADARO, SANTI DOMENICO
2009

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.
Settore MAT/03 - Geometria
https://reader.elsevier.com/reader/sd/pii/S0166864108003283?token=2547E5922FCB929DE2F88EE412DC202059F8891984E87FC521592FE597902C5A85FFB7C59BF54F221E898E8CABC1F991
SPADARO, S.D. (2009). Covering by discrete and closed discrete sets. TOPOLOGY AND ITS APPLICATIONS, 156(4), 721-727 [10.1016/j.topol.2008.09.009].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480954
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