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Mat. Sb., 1995, Volume 186, Number 3, Pages 19–28 (Mi msb19)  

This article is cited in 1 scientific paper (total in 1 paper)

Topological properties of extreme points of convex compact sets in $\ell^2$

E. M. Bronshtein

Ufa State Aviation Technical University

Abstract: Under certain restrictions on given sets $M$ and $K$, where $M\subset K$ and $K$ is a metric compact set, a continuous map $\varepsilon\colon K\to\ell^2$ is constructed such that $\operatorname{ext}\operatorname{conv}\varepsilon(K)=\varepsilon(M)$ and the restriction of $\varepsilon$ to $M$ is a topological embedding. Here $\operatorname{ext}$ is the set of extreme points and $\operatorname{conv}$ is the closed convex hull.

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English version:
Sbornik: Mathematics, 1995, 186:3, 327–336

Bibliographic databases:

UDC: 513.88
MSC: 46A55, 52A07
Received: 25.05.1994

Citation: E. M. Bronshtein, “Topological properties of extreme points of convex compact sets in $\ell^2$”, Mat. Sb., 186:3 (1995), 19–28; Sb. Math., 186:3 (1995), 327–336

Citation in format AMSBIB
\Bibitem{Bro95}
\by E.~M.~Bronshtein
\paper Topological properties of extreme points of convex compact sets in $\ell^2$
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 3
\pages 19--28
\mathnet{http://mi.mathnet.ru/msb19}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1331806}
\zmath{https://zbmath.org/?q=an:0856.46004}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 3
\pages 327--336
\crossref{https://doi.org/10.1070/SM1995v186n03ABEH000019}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ92200002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. M. Bronshtein, “Extreme Points of Convex Compact Sets in the Hilbert Cube”, Funct. Anal. Appl., 30:4 (1996), 273–275  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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