A fake topological Hilbert space
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- by R. D. Anderson, D. W. Curtis and J. van Mill
- Trans. Amer. Math. Soc. 272 (1982), 311-321
- DOI: https://doi.org/10.1090/S0002-9947-1982-0656491-8
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Abstract:
We give an example of a topologically complete separable metric AR space $X$ which is not homeomorphic to the Hilbert space ${l^2}$, but which has the following properties: (i) $X$ imbeds as a convex subset of ${l^2}$ (ii) every compact subset of $X$ is a $Z$-set; (iii) $X \times X \approx {l^2};$ (iv) $X$ is homogeneous; (v) $X \approx X\backslash G$ for every countable subset $G$.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 272 (1982), 311-321
- MSC: Primary 57N17; Secondary 46C05, 54G20, 57N20
- DOI: https://doi.org/10.1090/S0002-9947-1982-0656491-8
- MathSciNet review: 656491