Continuous selections of multivalued maps with non-convex non-closed decomposable values
Continuous selections of multivalued maps with non-convex non-closed decomposable values
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DOI：
10.1070/sm1996v187n05abeh000131
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发表时间：
1996-06
影响因子：
0.8
通讯作者：
A. Tolstonogov
中科院分区：
文献类型：
--
作者：
A. Tolstonogov
区分出一类具有非凸非闭可分解值的多值映射，并证明了此类映射存在连续选择的定理。这类映射包含其值为博赫纳可积函数的巴拿赫空间中具有闭凸可分解值的连续多值映射的端点的多值映射。证明基于贝尔纲定理。已知闭凸集的端点集一般不是闭的。因此，本文的结果回答了具有非凸非闭值的多值映射存在连续选择的问题。
A class of multivalued maps with non-convex non-closed decomposable values is distinguished, and theorems are proved on the existence of continuous selections for such maps. This class contains multivalued maps whose values are extreme points of continuous multivalued maps with closed convex decomposable values in a Banach space of Bochner-integrable functions. The proofs are based on the Baire category theorem. It is known that the set of extreme points of a closed convex set is in general not closed. Hence the results or paper answer the question of the existence of continuous selections for multivalued maps with non-convex non-closed values.