Normality in products with a countable factor |
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Authors: | Paul J Szeptycki |
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Institution: | Department of Mathematics and Statistics, York University, Toronto, ON, Canada M3J 1P3 |
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Abstract: | The class of normal spaces that have normal product with every countable space is considered. A countably compact normal space X and a countable Y such that X×Y is not normal is constructed assuming CH. Also, ? is used to construct a perfectly normal countably compact X and a countable Y such that X×Y is not normal. The question whether a Dowker space can have normal product with itself is considered. It is shown that if X is Dowker and contains any countable non-discrete subspace, then X2 is not normal. It follows that a product of a Dowker space and a countable space is normal if and only if the countable space is discrete. If X is Rudin's ZFC Dowker space, then X2 is normal. An example of a Dowker space of cardinality ℵ2 with normal square is constructed assuming . |
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Keywords: | Normal space Products Dowker space Counter-examples Countably compact Countable spaces |
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