A rigid space whose square is the Hilbert space

Dijkstra, Jan J.

doi:10.1090/S0002-9939-1985-0766540-2

A rigid space whose square is the Hilbert space
HTML articles powered by AMS MathViewer

by Jan J. Dijkstra PDF

Proc. Amer. Math. Soc. 93 (1985), 118-120 Request permission

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

Fredric D. Ancel and S. Singh, Rigid finite-dimensional compacta whose squares are manifolds, Proc. Amer. Math. Soc. 87 (1983), no. 2, 342–346. MR 681845, DOI 10.1090/S0002-9939-1983-0681845-X
Fredric D. Ancel, Paul F. Duvall, and S. Singh, Rigid $3$-dimensional compacta whose squares are manifolds, Proc. Amer. Math. Soc. 88 (1983), no. 2, 330–332. MR 695269, DOI 10.1090/S0002-9939-1983-0695269-2
R. D. Anderson, D. W. Curtis, and J. van Mill, A fake topological Hilbert space, Trans. Amer. Math. Soc. 272 (1982), no. 1, 311–321. MR 656491, DOI 10.1090/S0002-9947-1982-0656491-8
Jan 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), no. 3, 597–600. MR 627701, DOI 10.1090/S0002-9939-1981-0627701-2
Jerzy Mogilski, CE-decomposition of $l_{2}$-manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 3-4, 309–314 (English, with Russian summary). MR 552055

Un théorème sur les continus

13