Geodesic
The AR-Property of the spaces of closed convex sets
Katsuro Sakai 1   ; Masato Yaguchi 2
1 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571 Japan
2 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571 Japan and Sakuragawa 2-3-22-502 Mito, 310-0801 Japan
Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 15-24 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\mathop{\rm Conv}_{\rm H}(X)$, $\mathop{\rm Conv}_{\rm AW}(X)$ and $\mathop{\rm Conv}_{\rm W}(X)$ 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 $\mathop{\rm Conv}_{\rm H}(X)$ and the space $\mathop{\rm Conv}_{\rm AW}(X)$ are AR. In case $X$ is separable, $\mathop{\rm Conv}_{\rm W}(X)$ is locally path-connected.
DOI : 10.4064/cm106-1-2
Keywords: mathop conv mathop conv mathop conv spaces non empty closed convex sets normed linear space admitting hausdorff metric topology attouch wets topology wijsman topology respectively every component mathop conv space mathop conv separable mathop conv locally path connected

Katsuro Sakai  1   ; Masato Yaguchi  2

1 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571 Japan
2 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571 Japan and Sakuragawa 2-3-22-502 Mito, 310-0801 Japan 
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Katsuro Sakai; Masato Yaguchi. The AR-Property of the spaces of closed convex sets. Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 15-24. doi: 10.4064/cm106-1-2

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