Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spacesстатья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:The Michael selection theorem is extended to the case of setvalued 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.