Closures of faces of compact convex sets

A. K. Roy

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 2, page 221-234
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Roy, A. K.. "Closures of faces of compact convex sets." Annales de l'institut Fourier 25.2 (1975): 221-234. <http://eudml.org/doc/74225>.

@article{Roy1975,
abstract = {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.},
author = {Roy, A. K.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {221-234},
publisher = {Association des Annales de l'Institut Fourier},
title = {Closures of faces of compact convex sets},
url = {http://eudml.org/doc/74225},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Roy, A. K.
TI - Closures of faces of compact convex sets
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 2
SP - 221
EP - 234
AB - 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.
LA - eng
UR - http://eudml.org/doc/74225
ER -

References

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  1. [1] E.M. ALFSEN, Compact convex sets and boundary integrals, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1971. Zbl0209.42601
  2. [2] E.M. ALFSEN, On the geometry of Choquet simplexes, Math. Scand., 15 (1964), 97-110. Zbl0189.42802
  3. [3] E.M. ALFSEN &amp; E.G. EFFROS, Structure in real Banach spaces, Part I &amp; II, Annals of Math., 96, No. 1 (1972), 98-173. Zbl0248.46019
  4. [4] L. ASIMOW, Exposed faces of dual cones and peak-set criteria for function spaces, Journal of Function Analysis, vol. 12, No. 4 (1973). Zbl0264.46021
  5. [5] F. DEUTSCH &amp; R.J. LINDAHL, Minimal extremal subsets of the unit sphere, Math. Annalen, 197 (1972). Zbl0223.46020
  6. [6] A.J. ELLIS, On faces of compact convex sets and their annihilators, Math. Annalen, 184 (1969). Zbl0184.34403
  7. [7] A.J. ELLIS, Split faces in function algebras, Math Annalen, 195 (1972). Zbl0215.48305
  8. [8] G. JAMESON, Nearly directed subspaces of partially ordered linear spaces, Proc. Edinburgh Math. Soc., (2) 16 (1968). Zbl0165.46804
  9. [9] J. KOHN, Barycentres of unique maximal measures, J. of Funct. Analysis, 6 (1970). Zbl0206.43002
  10. [10] A. LIMA, On continuous convex functions and split faces, Proc. London Math. Soc., (3) 25 (1972). Zbl0236.46024
  11. [11] A. LIMA, Closed faces with internal points, Preprint series — Matematisk institutt, Universiteteti Oslo (1972). Zbl0294.46044
  12. [12] J.N. McDONALD, Compact convex sets with the equal support property, Pac. J. of Math., vol. 37, No. 2 (1971). Zbl0217.16006
  13. [13] R. PHELPS, Lectures on Choquet's Theorem, Van Nostrand, Princeton (1960). Zbl0172.15603
  14. [14] M. RAJAGOPALAN &amp; A.K. ROY, Maximal core representing measures and generalized polytopes, Quart. J. of Math., Oxford, vol. 25, no. 99 (1974). Zbl0297.46042
  15. [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. Zbl0177.37603

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