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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: J. E. Vaughan
Journal: Proc. Amer. Math. Soc. 51 (1975), 203-208
MSC: Primary 54B10
MathSciNet review: 0370464
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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.

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Keywords: Metric, <!– MATH ${\omega _\mu }$ –> <IMG WIDTH="29" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\omega _\mu }$">-metrizable, normal, paracompact, nonnormal product spaces, linearly stratifiable, <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$P$">-spaces of K. Morita
Article copyright: © Copyright 1975 American Mathematical Society