The AR-Property of the spaces of closed convex sets
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
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
@article{10_4064_cm106_1_2,
author = {Katsuro Sakai and Masato Yaguchi},
title = {The {AR-Property} of the spaces of closed convex sets},
journal = {Colloquium Mathematicum},
pages = {15--24},
year = {2006},
volume = {106},
number = {1},
doi = {10.4064/cm106-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm106-1-2/}
}
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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