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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2013 Volume 94, Issue 5, Pages 643–647 (Mi mzm10331)

This article is cited 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.

UDC: 517.982.256

Received: 19.11.2010

DOI: 10.4213/mzm10331


 English version:
Mathematical Notes, 2013, 94:5, 605–608

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© Steklov Math. Inst. of RAS, 2025