The AR-Property of the spaces of closed convex sets
The AR-Property of the spaces of closed convex sets
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DOI：
10.4064/cm106-1-2
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发表时间：
2006
影响因子：
0.4
通讯作者：
K. Sakai;Masato Yaguchi
中科院分区：
文献类型：
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作者：
K. Sakai;Masato Yaguchi
设ConvH(X), ConvAW(X)和ConvW(X)分别为赋范线性空间X中承认Hausdorff度量拓扑，Attouch-Wets拓扑和Wijsman拓扑的所有非空闭凸集的空间。我们证明了ConvH(X)和空间ConvAW(X)的每个分量都是AR。当X可分时，ConvW(X)是局部路径连通的。
Let ConvH(X), ConvAW(X) and ConvW(X) be the spaces of all nonempty 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 ConvH(X) and the space ConvAW(X) are AR. In case X is separable, ConvW(X) is locally path-connected.