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Note on hereditary normality of product spaces

✍ Scribed by A. Okuyama; S. Watson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
397 KB
Volume
82
Category
Article
ISSN
0166-8641

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✦ Synopsis

In 1964 K. Morita introduced the concept of P(m)-spaces which characterized the normality of products with any metrizable space of weight < m. Especially, a topological space X is a normal P(No)-space if and only if X x Y is normal for any separable metrizable space Y. Okuyama (1991) introduced a similar notion of weak P(No)-spaces which concerned the paracompactness of products with any K-analytic space.

In this note, we show the difference of P(No)-spaces and weak P(No)-spaces, and also characterize a topological space X such that X x Y is hereditarily normal for any hereditarily normal, weak P(No)-space Y.

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