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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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?)

  • [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 metric spaces, Fund. Math. 48 (1959/1960), 1–14. MR 0114203 (22 #5028)
  • [4] Jun-iti Nagata, A remark on general imbedding theorems in dimension theory, Proc. Japan Acad. 39 (1963), 197–199. MR 0164319 (29 #1616)
  • [5] -, Modern dimension theory, Groningen, 1965.
  • [6] Elżbieta Pol, On the dimension of the product of metrizable spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 6, 525–534 (English, with Russian summary). MR 511956 (80f:54032)

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Additional Information

PII: S 0002-9939(1988)0955024-7
Keywords: Countable dimensional, universal space, metric space, Hilbert space
Article copyright: © Copyright 1988 American Mathematical Society