Nonnormal products of 𝜔_{𝜇}-metrizable spaces

Autor:	J. E. Vaughan
Rok vydání:	1975
Předmět:	Discrete mathematics Pure mathematics Applied Mathematics General Mathematics media_common.quotation_subject Metric space Metrization theorem Product (mathematics) Metric (mathematics) Countable set Paracompact space Normal space Normality media_common Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 51:203-208
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-1975-0370464-6
Popis:	We describe a metric space X X and an ω 1 {\omega _1} -metrizable space Y Y whose product X × Y 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 ( m ) P(\mathfrak {m}) -spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1d70ff23f9c1926cd2c5a38d87a57ae2 https://doi.org/10.1090/s0002-9939-1975-0370464-6 Zobrazit plný text záznamu