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EnglishSay 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.
| Titolo: | Covering by discrete and closed discrete sets. |
| Autori interni: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/20.500.11769/244518 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/20.500.11769/244518
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