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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 6, Pages 16–19 (Mi vmumm540)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Bounded strict solar property of strict suns in the space $C(Q)$

A. R. Alimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The intersection of a sun $M$ in $C(Q)$ with a closed span $\Pi\subset C(Q) $ (in particular, with a closed ball) is shown to be a strict protosun, provided that the natural condition $M\cap\operatorname{int}\Pi\ne\varnothing$ is satisfied. This property is shown to characterize closed spans in $C(Q)$.

Key words: strict sun, strict protosun, sun, interval of functions, span, normed linear space.

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English version:
Moscow University Mathematics Bulletin, 2013, 68:1, 14–17

Bibliographic databases:

Document Type: Article
UDC: 517.982.252+517.982.256
Received: 05.10.2011

Citation: A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 6, 16–19; Moscow University Mathematics Bulletin, 68:1 (2013), 14–17

Citation in format AMSBIB
\Bibitem{Ali12}
\by A.~R.~Alimov
\paper Bounded strict solar property of strict suns in the space $C(Q)$
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 6
\pages 16--19
\mathnet{http://mi.mathnet.ru/vmumm540}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2013
\vol 68
\issue 1
\pages 14--17
\crossref{https://doi.org/10.3103/S0027132213010038}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874990898}


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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, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454  mathnet  crossref
    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, 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
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