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Proceedings of the American Mathematical Society

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Universal spaces for countable-dimensional metric spaces

Author: Tatsuo Goto
Journal: Proc. Amer. Math. Soc. 103 (1988), 1290-1292
MSC: Primary 54F45; Secondary 54E35
MathSciNet review: 955024
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Abstract: Let $ H(A)$ be the Dowker's generalized Hilbert space with weight $ \vert A\vert$, where $ A$ is any infinite set, and $ H\infty (A)$ its subspace consisting of all points which have only finitely many rational coordinates distinct from zero. Using a result of E. Pol, it will be shown that $ H\infty (A)$ is a universal space for countable dimensional metric spaces with weight $ \leq \vert A\vert$.

References [Enhancements On Off] (What's this?)

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Keywords: Countable dimensional, universal space, metric space, Hilbert space
Article copyright: © Copyright 1988 American Mathematical Society