Existence of selections and disconnectedness properties for the hyperspace of an ultrametric space
Existence of selections and disconnectedness properties for the hyperspace of an ultrametric space
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超度量空间的超空间的选择和断开属性的存在性
DOI：
10.1016/s0166-8641(97)00175-2
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发表时间：
1998
影响因子：
0.6
通讯作者：
C. Costantini
中科院分区：
文献类型：
--
作者：
D. Bertacchi;C. Costantini
刻画了Wijsman超空间允许连续选择的可分离完全超度量空间；这样的研究与V. Gutev关于球超空间的类似结果密切相关。表征可以根据基空间（X, d）（条件（#））或Wijsman超空间本身（完全不连通）的适当性质获得。给出了（可分）超度量空间的Wijsman超空间为零维的一个充分必要条件，并给出了该超空间为连通的一个例子。
We characterize the separable complete ultrametric spaces whose Wijsman hyperspace admits a continuous selection; such an investigation is closely connected to a similar result of V. Gutev about the Ball hyperspace. The characterization may be obtained in terms of a suitable property either of the base space (X, d) (condition (#)) or of the Wijsman hyperspace itself (total disconnectedness). We also give a necessary and sufficient condition for the zero-dimensionality of the Wijsman hyperspace of a (separable) ultrametric space, and we provide an example where such a hyperspace turns out to be connected.