A “hidden” characterization of polyhedral convex sets

Tom 206 / 2011

Taras Banakh, Ivan Hetman Studia Mathematica 206 (2011), 63-74 MSC: Primary 46A55, 52A07; Secondary 52B05, 52A37. DOI: 10.4064/sm206-1-5

Streszczenie

We prove that a closed convex subset $C$ of a complete linear metric space $X$ is polyhedral in its closed linear hull if and only if no infinite subset $A\subset X\setminus C$ can be hidden behind $C$ in the sense that $[x,y]\cap C\not = \emptyset $ for any distinct $x,y\in A$.

Autorzy

  • Taras BanakhIvan Franko National University of Lviv
    Ukraine
    and
    Jan Kochanowski University
    Kielce, Poland
    e-mail
  • Ivan HetmanIvan Franko National University of Lviv
    Universytetska 1
    Lviv, 79000, Ukraine
    e-mail

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