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On Banach-Mazur compacta

Part of: Special properties Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

Sergei M. Ageev  and
Duŝan Repovŝ
Sergei M. Ageev
Affiliation:
Department of Mathematics Brest Sates UniversityBrest 224665Belorussia e-mail: ageev@kiipm.belpak.brest.by
Duŝan Repovŝ
Affiliation:
Department of Mathematics University of LjubljanaLjubljana 1001Slovenia e-mail: dusan.repovs@fmf.uni-lj.si
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Abstract

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We study Banach-Mazur compacta Q(n), that is, the sets of all isometry classes of n-dimensional Banach spaces topologized by the Banach-Mazur metric. Our main result is that Q(2) is homeomorphic to the compactification of a Hilbert cube manifold by a point, for we prove that Qg(2) = Q(2) / {Eucl.} is a Hilbert cube manifold. As a corollary it follows that Q(2) is not homogeneous.

Keywords

noncompact Lie groupapproximate G-ANE spaceconvex G-spaceproper G-spaceBanach-Mazur compactum

MSC classification

Secondary: 57S10: Compact groups of homeomorphisms 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 54F45: Dimension theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 316 - 335
Copyright
Copyright © Australian Mathematical Society 2000

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