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 ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-1-5,
author = {Taras Banakh and Ivan Hetman},
title = {A "hidden" characterization of polyhedral convex sets},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {63-74},
zbl = {1235.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-1-5}
}
Taras Banakh; Ivan Hetman. A "hidden" characterization of polyhedral convex sets. Studia Mathematica, Tome 204 (2011) pp. 63-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-1-5/