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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

    A. R. Alimov

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  1. A. R. Alimov
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Correspondence to A. R. Alimov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 7, pp. 3–14, 2011/12.

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Alimov, A.R. Local Solarity of Suns in Normed Linear Spaces. J Math Sci 197, 447–454 (2014). https://doi.org/10.1007/s10958-014-1726-1

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