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A note on isomorphic groups and nonhomeomorphic spaces

Cuchillo Ibáñez, Eduardo and Morón, Manuel A. and Romero Ruiz del Portal, Francisco (1999) A note on isomorphic groups and nonhomeomorphic spaces. Acta Mathematica Hungarica, 82 (4). pp. 297-300. ISSN 0236-5294

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Abstract

Given a Tychonov space X we can construct another space Y with the same group of homeomorphisms such that X and Y are: in some sense, "almost arbitrarily different".

Item Type:Article
Uncontrolled Keywords:Isomorphic groups; nonhomeomorphic spaces; homeomorphisms; topological spaces
Subjects:Sciences > Mathematics > Group Theory
Sciences > Mathematics > Topology
ID Code:15522
References:

E. Cuchillo-Ibáñez, M. A. Morón and F. R. Ruiz del Portal, Lower semifinite topology in hyperspaces, Top. Proc. 17 (1992), 29-39.

R. Engelking, General Topology, P. N. W. (Warszawa, 1977).

R. A. McCoy, Homeomorphism groups of Hilbert cube manifolds, General Topology Appl.,2 (1972), 55-60.

E. Michael, Topology on spaces of subsets, Trans. A.M.S., 71 (1951), 152-182.

M. Rubin, On the reconstruction of topological spaces from their groups of homeomorphisms, Trans. A.M.S., 312 (1989), 487-538.

J. van Mills, Infinite-dimensional Topology, North-Holland (Amsterdam, 1989).

J. V. Whittaker, On isomorphic groups and homeomorphic spaces, Ann. of Math., 78 (1963),74-91.

Deposited On:07 Jun 2012 08:24
Last Modified:06 Feb 2014 10:26

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