Nonnormal products of $\omega _{\mu }$-metrizable spaces

Abstract:

We describe a metric space $X$ and an ${\omega _1}$-metrizable space $Y$ whose product $X \times Y$ is not normal. This provides another example to show that the product of a metric space with a normal space need not be normal. The first example of this nature was given by E. Michael, and we compare our example to his. We use our example to answer several questions concerning the normality of finite products of linearly stratifiable spaces, and countable products of hereditarily paracompact spaces. We also use some related examples to answer a question of K. Morita concerning $P(\mathfrak {m})$-spaces.