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On a certain class of $ M\sb{1}$-spaces


Author: T. Mizokami
Journal: Proc. Amer. Math. Soc. 87 (1983), 357-362
MSC: Primary 54E20; Secondary 54E15
MathSciNet review: 681849
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Abstract: Let $ \mathcal{P}$ be the class of all $ {M_1}$-spaces whose every closed subset has a closure-preserving open neighborhood base. A characterization is given, and it is proved that the adjunction space $ X{ \cup _f}Y$ is an $ {M_1}$-space if $ X \in \mathcal{P}$ and $ Y$ is an $ {M_1}$-space. Moreover, it is proved that if $ X$ is a space such that for each metrizable space $ Y$, every closed subspace of $ X \times Y$ is an $ {M_1}$-space, then $ X \in \mathcal{P}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0681849-7
Keywords: Stratifiable, $ {M_1}$-space, irreducible mapping, adjunction space, property ECP
Article copyright: © Copyright 1983 American Mathematical Society