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Transactions of the American Mathematical Society

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On first countable, countably compact spaces. I. $ (\omega \sb{1},\,\omega \sp{\ast} \sb{1})$-gaps

Authors: Peter J. Nyikos and Jerry E. Vaughan
Journal: Trans. Amer. Math. Soc. 279 (1983), 463-469
MSC: Primary 54A35; Secondary 03E35, 03E50, 54D15
MathSciNet review: 709563
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Abstract: This paper is concerned with the $ ({\omega_1},\omega_1^{\ast})$-gaps of F. Hausdorff and the topological spaces defined from them by Eric van Douwen. We construct special gaps in order that the associated gap spaces will have interesting topological properties. For example, the gap spaces we construct show that in certain models of set theory, there exist countably compact, first countable, separable, nonnormal $ {T_2}$-spaces.

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Keywords: First countable, countably compact, separable, nonnormal, zero-dimensional, $ ({\omega_1},\omega_1^{\ast})$-gaps, Hausdorff gaps, tight gaps, big gaps, continuum hypothesis, Martin's Axiom
Article copyright: © Copyright 1983 American Mathematical Society

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