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The AR-Property of the spaces of closed convex sets

Tom 106 / 2006

Katsuro Sakai, Masato Yaguchi Colloquium Mathematicum 106 (2006), 15-24 MSC: 54B20, 54C55, 46A55. DOI: 10.4064/cm106-1-2

Streszczenie

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.

Autorzy

  • Katsuro SakaiInstitute of Mathematics
    University of Tsukuba
    Tsukuba, 305-8571 Japan
    e-mail
  • Masato YaguchiInstitute of Mathematics
    University of Tsukuba
    Tsukuba, 305-8571 Japan
    and
    Sakuragawa 2-3-22-502
    Mito, 310-0801 Japan
    e-mail

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