Closures of faces of compact convex sets
Annales de l'Institut Fourier, Tome 25 (1975) no. 2, pp. 221-234.

Dans cet article nous étudions des conditions nécessaires et suffisantes pour que la fermeture d’une face d’un convexe compact soit encore une face. Comme applications des résultats, nous démontrons d’une manière uniforme quelques théorèmes qui sont dispersés dans la littérature.

This paper gives necessary and sufficient conditions for the closure of a face in a compact convex set to be again a face. As applications of these results, several theorems scattered in the literature are proved in an economical and uniform manner.

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     title = {Closures of faces of compact convex sets},
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Roy, A. K. Closures of faces of compact convex sets. Annales de l'Institut Fourier, Tome 25 (1975) no. 2, pp. 221-234. doi : 10.5802/aif.563. http://archive.numdam.org/articles/10.5802/aif.563/

[1] E.M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1971. | Zbl

[2] E.M. Alfsen, On the geometry of Choquet simplexes, Math. Scand., 15 (1964), 97-110. | Zbl

[3] E.M. Alfsen & E.G. Effros, Structure in real Banach spaces, Part I & II, Annals of Math., 96, No. 1 (1972), 98-173. | Zbl

[4] L. Asimow, Exposed faces of dual cones and peak-set criteria for function spaces, Journal of Function Analysis, vol. 12, No. 4 (1973). | Zbl

[5] F. Deutsch & R.J. Lindahl, Minimal extremal subsets of the unit sphere, Math. Annalen, 197 (1972). | Zbl

[6] A.J. Ellis, On faces of compact convex sets and their annihilators, Math. Annalen, 184 (1969). | Zbl

[7] A.J. Ellis, Split faces in function algebras, Math Annalen, 195 (1972). | Zbl

[8] G. Jameson, Nearly directed subspaces of partially ordered linear spaces, Proc. Edinburgh Math. Soc., (2) 16 (1968). | Zbl

[9] J. Kohn, Barycentres of unique maximal measures, J. of Funct. Analysis, 6 (1970). | Zbl

[10] A. Lima, On continuous convex functions and split faces, Proc. London Math. Soc., (3) 25 (1972). | Zbl

[11] A. Lima, Closed faces with internal points, Preprint series — Matematisk institutt, Universiteteti Oslo (1972). | Zbl

[12] J.N. Mcdonald, Compact convex sets with the equal support property, Pac. J. of Math., vol. 37, No. 2 (1971). | Zbl

[13] R. Phelps, Lectures on Choquet's Theorem, Van Nostrand, Princeton (1960).

[14] M. Rajagopalan & A.K. Roy, Maximal core representing measures and generalized polytopes, Quart. J. of Math., Oxford, vol. 25, no. 99 (1974). | Zbl

[15] M. Rogalski, Etude du quotient d'un simplexe par une face fermée... relation d'équivalence, Seminaire Brelot — Choquet — Deny (Theorie du Potentiel), 1967/1968, No. 2. | Numdam | Zbl

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