空间和有限维多面体空间中集合的Solarity和connectedness

Pub Date : 2022-01-01 DOI:10.1070/SM9554

I. G. Tsar’kov

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引用次数: 3

摘要

研究了由给定空间的单调路径连通有界紧子集构造的广义分段函数。它们被证明是单调的路径连接的太阳。在有限维多面体空间中，研究了允许下半连续选择度量投影算子的集合的光度点。构造了四维多面体赋范空间中无连通太阳的一个例子。参考书目:14篇。

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Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces

Generalized -piecewise functions constructed from given monotone path-connected boundedly compact subsets of the space are studied. They are shown to be monotone path-connected suns. In finite-dimensional polyhedral spaces, luminosity points of sets admitting a lower semicontinuous selection of the metric projection operator are investigated. An example of a non- -connected sun in a four-dimensional polyhedral normed space is constructed. Bibliography: 14 titles.

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