A fake topological Hilbert space

Anderson, R. D.; Curtis, D. W.; van Mill, J.

doi:10.1090/S0002-9947-1982-0656491-8

A fake topological Hilbert space
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by R. D. Anderson, D. W. Curtis and J. van Mill PDF

Trans. Amer. Math. Soc. 272 (1982), 311-321 Request permission

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 $G$.

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A counter-example in

-manifold theory

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