This article is cited in 7 scientific papers (total in 7 papers)
Local solarity of suns in normed linear spaces
A. R. Alimov
M. V. Lomonosov Moscow State University
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 $\mathrm m$-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.
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Journal of Mathematical Sciences (New York), 2014, 197:4, 447–454
A. R. Alimov, “Local solarity of suns in normed linear spaces”, Fundam. Prikl. Mat., 17:7 (2012), 3–14; J. Math. Sci., 197:4 (2014), 447–454
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\paper Local solarity of suns in normed linear spaces
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
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A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655
A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928
A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
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