Short proofs of two theorems in topology

Mohammad Ismail; Andrzej Szymański

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Displaying similar documents to “Short proofs of two theorems in topology”

A countably compact, separable space which is not absolutely countably compact

Jerry E. Vaughan (1995)

Commentationes Mathematicae Universitatis Carolinae

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We construct a space having the properties in the title, and with the same technique, a countably compact $T_{2}$ topological group which is not absolutely countably compact.

Absolute countable compactness of products and topological groups

Yan-Kui Song (1999)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].