The Normality in Products with a Countably Compact Factor

Abstract

ABSTRACT. It is known that the product°1 ðX of°1 with an M 1 -space may be nonnormal. In this paper we prove that the product îðX of an uncountable regular cardinal î 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.