Citation
Sm. Ageev et D. Repovs, On Banach-Mazur compacta, J AUS MAT A, 69, 2000, pp. 316-335
Citations number
25
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115
→ ACNP
Volume
69
Year of publication
2000
Part
3
Pages
316 - 335
Database
ISI
SICI code
0263-6115(200012)69:<316:OBC>2.0.ZU;2-F
Abstract
We study Banach-Mazur compacta Q(n), that is, the sets of all isometry clas
ses 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 H
ilbert cube manifold by a point, for we prove that Qs(2) = Q(2) \ {Eucl.} i
s a Hilbert cube manifold. As a corollary it follows that Q(2) is not homog
eneous.