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Cartesian products of metric Baire spaces


Author: M. R. Krom
Journal: Proc. Amer. Math. Soc. 42 (1974), 588-594
MSC: Primary 54C50; Secondary 04A30, 54E35, 90D05
DOI: https://doi.org/10.1090/S0002-9939-1974-0334138-9
MathSciNet review: 0334138
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Abstract: For any topological space X there is an associated ultrametric space $ \mathcal{U}(X)$ such that the cartesian product $ \mathcal{U}(X) \times Y$ with any other space Y is a Baire space iff $ X \times Y$ is a Baire space. Assuming the continuum hypothesis, there exists an indeterminate infinite two person game such that a cartesian product of the game with itself is determinate.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0334138-9
Keywords: Baire space, Baire category theorem, topological product, axiom of choice, continuum hypothesis, infinite game, determinate game, metric space, ultrametric space
Article copyright: © Copyright 1974 American Mathematical Society

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