Topological classification of closed convex sets in Frechet spaces

Details Topological classification of closed convex sets in Frechet spaces Topological classification of closed convex sets in Frechet spaces

2010-06-15

arxiv.org/abs/1006.3092v1

Studia Math. 205 (2011), 1-11

Mathematics

Functional Analysis

8 pages

Scientific paper

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 $k\ge 0$.

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