Covering by discrete and closed discrete sets |
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Authors: | Santi Spadaro |
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Institution: | Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL 36849-5310, USA |
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Abstract: | Say 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. |
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Keywords: | primary 54A25 secondary 54E52 54E18 54E30 54F05 |
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