Local solarity of suns in normed linear spacesстатья
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Статья опубликована в журнале из перечня ВАК
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Дата последнего поиска статьи во внешних источниках: 18 июля 2016 г.
Аннотация:The paper is concerned with solarity of intersections of suns with bars (in particular, with closed balls and extreme hyperstrips) in normed linear spaces. A sun in a finite-dimensional (BM)-space (in particular, in $l^1(n)$) is shown to be monotone path connected. A nonempty intersection of an m-connected set (in particular, a sun in a two-dimensional space or in a finite-dimensional (BM)-space) with a bar is shown to be a monotone path-connected sun. Similar results are obtained for boundedly compact subsets of infinite-dimensional spaces. A nonempty intersection of a monotone path-connected subset of a normed space with a bar is shown to be a monotone path-connected $\alpha$-sun