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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonnormal products of $\omega _{\mu }$-metrizable spaces
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by J. E. Vaughan PDF
Proc. Amer. Math. Soc. 51 (1975), 203-208 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 203-208
  • MSC: Primary 54B10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0370464-6
  • MathSciNet review: 0370464