The Banach-Mazur compactum BM(2) is homeomorphic to the orbit space (exp S-1)/O(2)

Abstract

We prove a general theorem about the orbit spaces of compact Lie group actions which are Hilbert cube manifolds. This result is further applied to prove that the Banach-Mazur compactum BM(2) is homeomorphic to the orbit space (expS(1))/O(2), where exp S-1 is the hyperspace of all nonempty closed subsets of the unit circle S 1 endowed with the induced action of the orthogonal group O(2). (C) 2006 Elsevier B.V. All rights reserved.