# Local Solarity of Suns in Normed Linear Spaces

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## Abstract

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 *α*-sun.

## Keywords

Closed Ball Normed Linear Space Separable Banach Space Nonempty Intersection Converse Assertion
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