On a certain class of $M_{1}$-spaces
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- by T. Mizokami PDF
- Proc. Amer. Math. Soc. 87 (1983), 357-362 Request permission
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 $X \in \mathcal {P}$.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 357-362
- MSC: Primary 54E20; Secondary 54E15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0681849-7
- MathSciNet review: 681849