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The Normality in Products with a Countably Compact Factor
Published online by Cambridge University Press: 20 November 2018
Abstract
It is known that the product ${{\omega }_{1}}\times X$ of
${{\omega }_{1}}$ with an
${{M}_{1}}$-space may be non-normal. In this paper we prove that the product
$\kappa \times X$ of an uncountable regular cardinal κ with a paracompact semi-stratifiable space is normal iff 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.
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- Copyright © Canadian Mathematical Society 1998