Topological classification of closed convex sets in Fréchet spaces

Tom 205 / 2011

Taras Banakh, Robert Cauty Studia Mathematica 205 (2011), 1-11 MSC: Primary 57N17; Secondary 46A55. DOI: 10.4064/sm205-1-1

Streszczenie

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 $[0,1]^n\times [0,1)^m\times \ell _2(\kappa )$ for some cardinals $0\le n\le \omega $, $0\le m\le 1$ and $\kappa \ge 0$.

Autorzy

  • Taras BanakhWydział Matematyczno-Przyrodniczy
    Uniwersytet Jana Kochanowskiego
    Świętokrzyska 15
    25-406 Kielce, Poland
    and
    Department of Mathematics
    Ivan Franko National University of Lviv
    Universytetska 1
    79000 Lviv, Ukraine
    e-mail
  • Robert CautyFaculté de Mathématiques
    Université Paris VI
    4, place Jussieu
    75005 Paris, France
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek