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Mat. Zametki, 2013, Volume 94, Issue 5, Pages 643–647 (Mi mz10331)  

This article is cited in 2 scientific papers (total in 2 papers)

Examples of Sets with Given Approximation Properties in $WCG$-Space

P. A. Borodin

M. V. Lomonosov Moscow State University

Abstract: An example of a nontrivial convex bounded Chebyshev set is constructed in an arbitrary weakly compactly generated Banach space ($WCG$-space). An example of bounded approximately compact but not locally compact set is constructed in an arbitrary infinite-dimensional $WCG$-space.

Keywords: approximative compactness, weakly compactly generated Banach space, locally compact set, Chebyshev set.

DOI: https://doi.org/10.4213/mzm10331

Full text: PDF file (403 kB)
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English version:
Mathematical Notes, 2013, 94:5, 605–608

Bibliographic databases:

UDC: 517.982.256
Received: 19.11.2010

Citation: P. A. Borodin, “Examples of Sets with Given Approximation Properties in $WCG$-Space”, Mat. Zametki, 94:5 (2013), 643–647; Math. Notes, 94:5 (2013), 605–608

Citation in format AMSBIB
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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, 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
    2. 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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