Cardinality of discrete subsets of a topological space
In this paper we prove two results relating the cardinalities of discrete subsets to those of dense subsets of a topological space. In particular, we show that (1) closed discrete subsets of separable normal spaces are countable, and (2) discrete subsets of separable regular spaces have cardinalitie...
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| Veröffentlicht in: | Bulletin of the Australian Mathematical Society 1982-02, Vol.25 (1), p.99-101 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we prove two results relating the cardinalities of discrete subsets to those of dense subsets of a topological space. In particular, we show that (1) closed discrete subsets of separable normal spaces are countable, and (2) discrete subsets of separable regular spaces have cardinalities at most that of the continuum. |
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| ISSN: | 0004-9727 1755-1633 |
| DOI: | 10.1017/S0004972700005074 |