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August 2010 Dowker spaces revisited
Lewis D. Ludwig, Peter Nyikos, John E. Porter
Tsukuba J. Math. 34(1): 1-11 (August 2010). DOI: 10.21099/tkbjm/1283967404

Abstract

In 1951, Dowker proved that a space $X$ is countably paracompact and normal if and only if $X \times {\bf I}$ is normal. A normal space $X$ is called a Dowker space if $X \times {\bf I}$ is not normal. The main thrust of this article is to extend this work with regards $\alpha$-normality and $\beta$-normality. Characterizations are given for when the product of a space $X$ and $(\omega + 1)$ is $\alpha$-normal or $\beta$-normal. A new definition, $\alpha$-countably paracompact, illustrates what can be said if the product of $X$ with a compact metric space is $\beta$-normal. Several examples demonstrate that the product of a Dowker space and a compact metric space may or may not be $\alpha$-normal or $\beta$-normal. A collectionwise Hausdorff. Moore space constructed by M. Wage is shown to be $\alpha$-normal but not $\beta$-nornal.

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Lewis D. Ludwig. Peter Nyikos. John E. Porter. "Dowker spaces revisited." Tsukuba J. Math. 34 (1) 1 - 11, August 2010. https://doi.org/10.21099/tkbjm/1283967404

Information

Published: August 2010
First available in Project Euclid: 8 September 2010

zbMATH: 1203.54015
MathSciNet: MR2723720
Digital Object Identifier: 10.21099/tkbjm/1283967404

Subjects:
Primary: 54D15

Keywords: $\alpha$-countably paracompact , $\alpha$-normal , $\beta$-normal , Dowker , Moore spaces , products

Rights: Copyright © 2010 University of Tsukuba, Institute of Mathematics

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Vol.34 • No. 1 • August 2010
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