1Institute of Mathematics University of Tsukuba Tsukuba, 305-8571 Japan 2Institute 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
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.
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
Affiliations des auteurs :
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
