The AR-Property of the spaces of closed convex sets

Katsuro Sakai, and Masato Yaguchi. "The AR-Property of the spaces of closed convex sets." Colloquium Mathematicae 106.1 (2006): 15-24. <http://eudml.org/doc/284055>.

@article{KatsuroSakai2006,
abstract = {Let $Conv_\{H\}(X)$, $Conv_\{AW\}(X)$ and $Conv_\{W\}(X)$ be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of $Conv_\{H\}(X)$ and the space $Conv_\{AW\}(X)$ are AR. In case X is separable, $Conv_\{W\}(X)$ is locally path-connected.},
author = {Katsuro Sakai, Masato Yaguchi},
journal = {Colloquium Mathematicae},
keywords = {the space of closed convex sets; normed linear space; Hausdorff metric; Attouch–Wets topology; Wijsman topology; AR; uniform AR; homotopy dense; locally path-connected},
language = {eng},
number = {1},
pages = {15-24},
title = {The AR-Property of the spaces of closed convex sets},
url = {http://eudml.org/doc/284055},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Katsuro Sakai
AU - Masato Yaguchi
TI - The AR-Property of the spaces of closed convex sets
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 15
EP - 24
AB - Let $Conv_{H}(X)$, $Conv_{AW}(X)$ and $Conv_{W}(X)$ be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of $Conv_{H}(X)$ and the space $Conv_{AW}(X)$ are AR. In case X is separable, $Conv_{W}(X)$ is locally path-connected.
LA - eng
KW - the space of closed convex sets; normed linear space; Hausdorff metric; Attouch–Wets topology; Wijsman topology; AR; uniform AR; homotopy dense; locally path-connected
UR - http://eudml.org/doc/284055
ER -