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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0955024-7
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?)

  • [1] C. H. Dowker, An imbedding theorem for paracompact metric spaces, Duke Math. J. 14 (1947), 639-645. MR 0022344 (9:196g)
  • [2] T. Goto, A note on the embeddings of metric spaces into generalized Hilbert spaces, J. Saitama Univ. 36 (1987), 1-3.
  • [3] J. Nagata, On the countable sum of zero-dimensional spaces, Fund. Math. 48 (1960), 1-14. MR 0114203 (22:5028)
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  • [6] E. Pol, On the dimension of the product of metrizable spaces, Bull. Acad. Polon. 26 (1976), 525-534. MR 511956 (80f:54032)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0955024-7
Keywords: Countable dimensional, universal space, metric space, Hilbert space
Article copyright: © Copyright 1988 American Mathematical Society

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