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Local solarity of suns in normed linear spaces. (English. Russian original) Zbl 1314.46018
J. Math. Sci., New York 197, No. 4, 447-454 (2014); translation from Fundam. Prikl. Mat. 17(2011/2012), No. 7, 3-14 (2012).
Summary: 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 \(\ell^1(n)\)) 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.

MSC:
46B20 Geometry and structure of normed linear spaces
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