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# The normality in products with a countably compact factor

Published:1998-06-01
Printed: Jun 1998
• Lecheng Yang
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## Abstract

It is known that the product $\omega_1 \times X$ of $\omega_1$ with an $M_1$-space may be nonnormal. In this paper we prove that the product $\kappa \times X$ of an uncountable regular cardinal $\kappa$ with a paracompact semi-stratifiable space is normal if{f} it is countably paracompact. We also give a sufficient condition under which the product of a normal space with a paracompact space is normal, from which many theorems involving such a product with a countably compact factor can be derived.
 MSC Classifications: 54B19 - unknown classification 54B1954D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.)