Closures of faces of compact convex sets
Roy, A. K.
Annales de l'Institut Fourier, Tome 25 (1975), p. 221-234 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

@article{AIF_1975__25_2_221_0,
     author = {Roy, A. K.},
     title = {Closures of faces of compact convex sets},
     journal = {Annales de l'Institut Fourier},
     volume = {25},
     year = {1975},
     pages = {221-234},
     doi = {10.5802/aif.563},
     mrnumber = {52 \#11537},
     zbl = {0282.52001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1975__25_2_221_0}
}

Roy, A. K. Closures of faces of compact convex sets. Annales de l'Institut Fourier, Tome 25 (1975) pp. 221-234. doi : 10.5802/aif.563. http://gdmltest.u-ga.fr/item/AIF_1975__25_2_221_0/

[1] E.M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1971. | Zbl 0209.42601

[2] E.M. Alfsen, On the geometry of Choquet simplexes, Math. Scand., 15 (1964), 97-110. | Zbl 0189.42802

[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 0248.46019

[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 0264.46021

[5] F. Deutsch & R.J. Lindahl, Minimal extremal subsets of the unit sphere, Math. Annalen, 197 (1972). | Zbl 0223.46020

[6] A.J. Ellis, On faces of compact convex sets and their annihilators, Math. Annalen, 184 (1969). | Zbl 0184.34403

[7] A.J. Ellis, Split faces in function algebras, Math Annalen, 195 (1972). | Zbl 0215.48305

[8] G. Jameson, Nearly directed subspaces of partially ordered linear spaces, Proc. Edinburgh Math. Soc., (2) 16 (1968). | Zbl 0165.46804

[9] J. Kohn, Barycentres of unique maximal measures, J. of Funct. Analysis, 6 (1970). | Zbl 0206.43002

[10] A. Lima, On continuous convex functions and split faces, Proc. London Math. Soc., (3) 25 (1972). | Zbl 0236.46024

[11] A. Lima, Closed faces with internal points, Preprint series — Matematisk institutt, Universiteteti Oslo (1972). | Zbl 0294.46044

[12] J.N. Mcdonald, Compact convex sets with the equal support property, Pac. J. of Math., vol. 37, No. 2 (1971). | Zbl 0217.16006

[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 0297.46042

[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 0177.37603