Geodesic
A “hidden” characterization of polyhedral convex sets
Taras Banakh1 ; Ivan Hetman2
1 Ivan Franko National University of Lviv Ukraine and Jan Kochanowski University Kielce, Poland
2 Ivan Franko National University of Lviv Universytetska 1 Lviv, 79000, Ukraine
Studia Mathematica, Tome 206 (2011) no. 1, pp. 63-74

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $x,y\in A$.
DOI : 10.4064/sm206-1-5
Keywords: prove closed convex subset complete linear metric space polyhedral its closed linear hull only infinite subset subset setminus hidden behind sense cap emptyset distinct

Taras Banakh 1 ; Ivan Hetman 2

1 Ivan Franko National University of Lviv Ukraine and Jan Kochanowski University Kielce, Poland
2 Ivan Franko National University of Lviv Universytetska 1 Lviv, 79000, Ukraine 
@article{10_4064_sm206_1_5,
     author = {Taras Banakh and Ivan Hetman},
     title = {A {\textquotedblleft}hidden{\textquotedblright} characterization of
 polyhedral convex sets},
     journal = {Studia Mathematica},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {206},
     number = {1},
     year = {2011},
     doi = {10.4064/sm206-1-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm206-1-5/}
}
TY  - JOUR
AU  - Taras Banakh
AU  - Ivan Hetman
TI  - A “hidden” characterization of
 polyhedral convex sets
JO  - Studia Mathematica
PY  - 2011
SP  - 63
EP  - 74
VL  - 206
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm206-1-5/
DO  - 10.4064/sm206-1-5
LA  - en
ID  - 10_4064_sm206_1_5
ER  - 
%0 Journal Article
%A Taras Banakh
%A Ivan Hetman
%T A “hidden” characterization of
 polyhedral convex sets
%J Studia Mathematica
%D 2011
%P 63-74
%V 206
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm206-1-5/
%R 10.4064/sm206-1-5
%G en
%F 10_4064_sm206_1_5
Taras Banakh; Ivan Hetman. A “hidden” characterization of
 polyhedral convex sets. Studia Mathematica, Tome 206 (2011) no. 1, pp. 63-74. doi: 10.4064/sm206-1-5

Cité par Sources :