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Proceedings of the American Mathematical Society

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On the dimension of cubic $ \mu $-spaces


Author: T. Mizokami
Journal: Proc. Amer. Math. Soc. 82 (1981), 291-298
MSC: Primary 54F45
DOI: https://doi.org/10.1090/S0002-9939-1981-0609670-4
MathSciNet review: 609670
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Abstract: Let $ X$ be the countable product of special $ \sigma $-metric spaces defined below. Then it is proved that $ X \leqslant n$ if and only if there exists a $ \sigma $-closure-preserving open base $ \mathcal{W}$ for $ X$ such that $ {\text{Ind}}\;B(W) \leqslant n - 1$ for every $ W \in \mathcal{W}$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609670-4
Keywords: $ \sigma $-metric space, $ \sigma $-closure-preserving open base, special scale
Article copyright: © Copyright 1981 American Mathematical Society

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