On Banach-Mazur compacta

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.} i...

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Veröffentlicht in:	Journal of the Australian Mathematical Society (2001) 2000-12, Vol.69 (3), p.316-335
Hauptverfasser:	Ageev, Sergei M., Repovŝ, Duŝan
Format:	Artikel
Sprache:	eng
Schlagworte:	54F45 approximate G-ANE space Banach-Mazur compactum convex G-space noncompact Lie group primary 57S10 proper G-space secondary 54C55
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Beschreibung
Zusammenfassung:	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.
ISSN:	0263-6115 1446-7887 1446-8107
DOI:	10.1017/S1446788700002494