On Collectionwise Normality of Product Spaces. II

Abstract

In this paper the following results will be obtained. (1) Let X be a closed image of a normal M-space and Y a paracompact first countable /"-space. If XX 7 is normal, then X X Y is collectionwise normal.(2) Let X be a collectionwise normal space and Y a a-locally compact paracompact space. If X X Y is normal, then Y x y is collectionwise normal.Theorem 2. Let X be a collectionwise normal space and Y a o-locally compact paracompact space and X X Y normal. Then XX Y is collectionwise normal.The definitions of M-spaces and P-spaces are due to Morita [7] and o-spaces are due to Okuyama [12].