This is an announcement for the paper "Topological classification of closed convex sets in Frechet spaces" by Taras Banakh and Robert Cauty.

Abstract: We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowoslki and Torunczyk, this result implies that each closed convex subset of a Frechet space is homemorphic to $[0,1]^n\times [0,1)^m\times l_2(k)$ for some cardinals $0\le n\le\omega$, $0\le m\le 1$ and $k\ge 0$.

Archive classification: math.FA math.GN math.GT

Mathematics Subject Classification: 57N17, 46A04

Remarks: 8 pages

Submitted from: tbanakh@yahoo.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1006.3092

or

http://arXiv.org/abs/1006.3092