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On the Cardinality of Urysohn Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 31 / Issue 2 / 01 June 1988
- Published online by Cambridge University Press:
- 20 November 2018, pp. 153-158
- Print publication:
- 01 June 1988
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- Article
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In this paper some cardinal inequalities for Urysohn spaces are established. In particular the following two theorems are proved:
(i)If
where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;(ii)
, where aL(X, X) is the smallest cardinal number m such that for every open cover 
of X there is a subfamily 
for which 
where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;
, where aL(X, X) is the smallest cardinal number m such that for every open cover 
of X there is a subfamily 
for which 
