The AR-Property of the spaces of closed convex sets

• Autorzy: Katsuro Sakai , Masato Yaguchi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 54B20: Hyperspaces
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 1
• Strony: 15-24

Daty

wydano

2006

Twórcy

autor

Katsuro Sakai

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

autor

Masato Yaguchi

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan
• Sakuragawa 2-3-22-502, Mito, 310-0801 Japan

Identyfikatory

DOI

10.4064/cm106-1-2