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Fundam. Prikl. Mat., 2012, Volume 17, Issue 7, Pages 3–14 (Mi fpm1454)  

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

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 $\ell^1(n)$) 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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English version:
Journal of Mathematical Sciences (New York), 2014, 197:4, 447–454

Document Type: Article
UDC: 517.982.256

Citation: 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

Citation in format AMSBIB
\Bibitem{Ali12}
\by A.~R.~Alimov
\paper Local solarity of suns in normed linear spaces
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 7
\pages 3--14
\mathnet{http://mi.mathnet.ru/fpm1454}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 197
\issue 4
\pages 447--454
\crossref{https://doi.org/10.1007/s10958-014-1726-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84893954252}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. 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  mathnet  crossref  mathscinet
    3. A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18  mathnet
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11  mathnet
    7. A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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