The AR-Property of the spaces of closed convex sets

Katsuro Sakai; Masato Yaguchi

Colloquium Mathematicae, Tome 106 (2006), p. 15-24 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $C o n v_{H} (X)$ , $C o n v_{A W} (X)$ and $C o n v_{W} (X)$ 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 $C o n v_{H} (X)$ and the space $C o n v_{A W} (X)$ are AR. In case X is separable, $C o n v_{W} (X)$ is locally path-connected.

Publié le : 2006-01-01

Zbl 1099.54013

EUDML-ID : urn:eudml:doc:284055

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Katsuro Sakai; Masato Yaguchi. The AR-Property of the spaces of closed convex sets. Colloquium Mathematicae, Tome 106 (2006) pp. 15-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-2/