Abstract:In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space $\sigma $. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a $\sigma $-compactum or not.
Keywords: Hilbert space, Hilbert cube, ${\Cal F_{\sigma \delta }}$-absorber, ambient homeomorphism, function space, $p$-summable sequence
AMS Subject Classification: 57N20