On Banach-Mazur compacta

Abstract

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 Qℰ (2) = Q(2) \ {Eucl.} is a Hilbert cube manifold. As a corollary it follows that Q(2) is not homogeneous.