Topological classification of closed convex sets in Frechet spaces

2010/06/15 by Taras Banakh, Robert Cauty · 1 citation
Mathematics · #math.FA #math.GN #math.GT #msc:57N17 #msc:46A04

paper · pdf

published as Studia Math. 205 (2011), 1-11 · 8 pages

arxiv created 2010/06/15 · arxiv updated 2011/10/11

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× [0,1)^m× l₂(k) for some cardinals 0≤ n≤ω, 0≤ m≤ 1 and k≥ 0.

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