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Cardinality of discrete subsets of a topological space
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 99 - 101
- Copyright
- Copyright © Australian Mathematical Society 1982
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