Universal spaces for countable-dimensional metric spaces
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- by Tatsuo Goto PDF
- Proc. Amer. Math. Soc. 103 (1988), 1290-1292 Request permission
Abstract:
Let $H(A)$ be the Dowker’s generalized Hilbert space with weight $|A|$, 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 $\leq |A|$.References
- C. H. Dowker, An imbedding theorem for paracompact metric spaces, Duke Math. J. 14 (1947), 639–645. MR 22344, DOI 10.1215/S0012-7094-47-01450-6 T. Goto, A note on the embeddings of metric spaces into generalized Hilbert spaces, J. Saitama Univ. 36 (1987), 1-3.
- J. Nagata, On the countable sum of zero-dimensional metric spaces, Fund. Math. 48 (1959/60), 1–14. MR 114203, DOI 10.4064/fm-48-1-1-14
- Jun-iti Nagata, A remark on general imbedding theorems in dimension theory, Proc. Japan Acad. 39 (1963), 197–199. MR 164319 —, Modern dimension theory, Groningen, 1965.
- 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
Additional Information
- © Copyright 1988 American Mathematical Society
- 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