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