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A rigid space whose square is the Hilbert space


Author: Jan J. Dijkstra
Journal: Proc. Amer. Math. Soc. 93 (1985), 118-120
MSC: Primary 54G15; Secondary 57N20
DOI: https://doi.org/10.1090/S0002-9939-1985-0766540-2
MathSciNet review: 766540
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Abstract: We construct a space $ X$ with only one autohomeomorphism and the property that the product $ X \times X$ is homeomorphic to the separable Hilbert space.


References [Enhancements On Off] (What's this?)

  • [1] F. D. Ancel and S. Singh, Rigid finite dimensional compacta whose squares are manifolds, Proc. Amer. Math. Soc. 87 (1983), 342-346. MR 681845 (83m:54074)
  • [2] F. D. Ancel, P. F. Duvall and S. Singh, Rigid $ 3$-dimensional compacta whose squares are manifolds, Proc. Amer. Math. Soc. 88 (1983), 330-332. MR 695269 (84m:54039)
  • [3] R. D. Anderson, D. W. Curtis and J. van Mill, A fake topological Hilbert space, Trans. Amer. Math. Soc. 272 (1982), 311-321. MR 656491 (83j:57009)
  • [4] J. van Mill, A rigid space $ X$ for which $ X \times X$ is homogeneous; an application of infinite-dimensional topology, Proc. Amer. Math. Soc. 83 (1981), 597-600. MR 627701 (82h:54067)
  • [5] J. Mogilski, $ CE$-decomposition of $ {l^2}$-manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 27 (1979), 309-314. MR 552055 (81e:57018)
  • [6] W. Sierpiński, Un théorème sur les continus, Tôhoku Math. J. 13 (1918), 300-303.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766540-2
Keywords: Rigid, Hilbert space, continuum-connected
Article copyright: © Copyright 1985 American Mathematical Society

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