Topological classification of closed convex sets in Fréchet spaces

• Autorzy: Taras Banakh , Robert Cauty
• Języki publikacji: EN

Abstrakty

EN

We prove that each non-separable completely metrizable convex subset of a Fréchet space is homeomorphic to a Hilbert space. This resolves a more than 30 years old problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowolski and Toruńczyk, this result implies that each closed convex subset of a Fréchet space is homeomorphic to $[0,1]ⁿ × [0,1)^{m} × ℓ₂(κ)$ for some cardinals 0 ≤ n ≤ ω, 0 ≤ m ≤ 1 and κ ≥ 0.

Kategorie tematyczne

• 57N17: Topology of topological vector spaces
• 46A55: Convex sets in topological linear spaces; Choquet theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 1
• Strony: 1-11

Daty

wydano

2011

Twórcy

autor

Taras Banakh

• Wydział Matematyczno-Przyrodniczy, Uniwersytet Jana Kochanowskiego, Świętokrzyska 15, 25-406 Kielce, Poland
• Department of Mathematics, Ivan Franko National University of Lviv, Universytetska 1, 79000 Lviv, Ukraine

autor

Robert Cauty

• Faculté de Mathématiques, Université Paris VI, 4, place Jussieu, 75005 Paris, France

Identyfikatory

DOI

10.4064/sm205-1-1