A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

Taras Banakh, and Ivan Hetman. "A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces." Studia Mathematica 210.2 (2012): 137-157. <http://eudml.org/doc/286095>.

@article{TarasBanakh2012,
abstract = {A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space $Conv_\{\}(X)$ of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex set.},
author = {Taras Banakh, Ivan Hetman},
journal = {Studia Mathematica},
keywords = {polyhedral convex set; approximatively polyhedral convex set; positively hiding convex set; infinitely hiding convex set; space of closed convex sets; Hausdorff metric},
language = {eng},
number = {2},
pages = {137-157},
title = {A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces},
url = {http://eudml.org/doc/286095},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Taras Banakh
AU - Ivan Hetman
TI - A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 2
SP - 137
EP - 157
AB - A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space $Conv_{}(X)$ of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex set.
LA - eng
KW - polyhedral convex set; approximatively polyhedral convex set; positively hiding convex set; infinitely hiding convex set; space of closed convex sets; Hausdorff metric
UR - http://eudml.org/doc/286095
ER -