非对称半线性空间中集值映射的连续选择与逼近

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9331e

Igor' Germanovich Tsar'kov

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引用次数: 0

摘要

将Michael选择定理推广到不一定具有凸值的集值映射。研究了具有对称半精和非对称半精的锥空间上的经典逼近问题。特别地，研究了非对称空间凸子集连续选择存在的条件。在具有Hausdorff半度量的有界凸集组成的半线性空间中，解决了有界凸集的Chebyshev中心的存在性问题。

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Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces

The Michael selection theorem is extended to the case of set-valued mappings with not necessarily convex values. Classical approximation problems on cone-spaces with symmetric and asymmetric seminorms are considered. In particular, conditions for existence of continuous selections for convex subsets of asymmetric spaces are studied. The problem of existence of a Chebyshev centre for a bounded set is solved in a semilinear space consisting of bounded convex sets with Hausdorff semimetric.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.