Products of $M$-spaces
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- by C. Bandy PDF
- Proc. Amer. Math. Soc. 45 (1974), 426-430 Request permission
Abstract:
The author associates with each pair $X,Y$ of $M$-spaces such that $X \times Y$ is not an $M$-space, a pair of countably compact closed subspaces $A \subset X,B \subset Y$ such that $A \times B$ is not countably compact, and for each pair $A,B$ of countably compact spaces whose product is not countably compact, there is a pair of $M$-spaces $S,T$ (in fact, $S$ and $T$ ate countably compact) such that $S \times T$ is not an $M$-space and such that $A$ and $B$ are closed subspaces of $S$ and $T$ respectively.References
- Takesi Isiwata, The product of $M$-spaces need not be an $M$-space, Proc. Japan Acad. 45 (1969), 154โ156. MR 244929
- Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365โ382. MR 165491, DOI 10.1007/BF01362570
- J. Novรกk, On the Cartesian product of two compact spaces, Fund. Math. 40 (1953), 106โ112. MR 60212, DOI 10.4064/fm-40-1-106-112
- A. K. Steiner, On the topological completion of $M$-space products, Proc. Amer. Math. Soc. 29 (1971), 617โ620. MR 282339, DOI 10.1090/S0002-9939-1971-0282339-8
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 426-430
- MSC: Primary 54E99
- DOI: https://doi.org/10.1090/S0002-9939-1974-0346759-8
- MathSciNet review: 0346759