The Normality in Products with a Countably Compact Factor

Abstract

AbstractIt is known that the product ω1 × X of ω1 with an M1-spacemay be nonnormal. In this paper we prove that the product κ × 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.