A note on intersections of simplices

David A. Edwards; Ondřej F. K. Kalenda; Jiří Spurný

Bulletin de la Société Mathématique de France (2011)

  • Volume: 139, Issue: 1, page 89-95
  • ISSN: 0037-9484

Abstract

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We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.

How to cite

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Edwards, David A., Kalenda, Ondřej F. K., and Spurný, Jiří. "A note on intersections of simplices." Bulletin de la Société Mathématique de France 139.1 (2011): 89-95. <http://eudml.org/doc/272428>.

@article{Edwards2011,
abstract = {We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.},
author = {Edwards, David A., Kalenda, Ondřej F. K., Spurný, Jiří},
journal = {Bulletin de la Société Mathématique de France},
keywords = {simplex; Bauer simplex; intersection; representing matrix},
language = {eng},
number = {1},
pages = {89-95},
publisher = {Société mathématique de France},
title = {A note on intersections of simplices},
url = {http://eudml.org/doc/272428},
volume = {139},
year = {2011},
}

TY - JOUR
AU - Edwards, David A.
AU - Kalenda, Ondřej F. K.
AU - Spurný, Jiří
TI - A note on intersections of simplices
JO - Bulletin de la Société Mathématique de France
PY - 2011
PB - Société mathématique de France
VL - 139
IS - 1
SP - 89
EP - 95
AB - We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.
LA - eng
KW - simplex; Bauer simplex; intersection; representing matrix
UR - http://eudml.org/doc/272428
ER -

References

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  1. [1] D. A. Edwards – « Systèmes projectifs d’ensembles convexes compacts », Bull. Soc. Math. France103 (1975), p. 225–240. Zbl0346.46002MR397359
  2. [2] V. P. Fonf, J. Lindenstrauss & R. R. Phelps – « Infinite dimensional convexity », in Handbook of the geometry of Banach spaces, Vol. I, North-Holland, 2001, p. 599–670. Zbl1086.46004MR1863703
  3. [3] A. J. Lazar & J. Lindenstrauss – « Banach spaces whose duals are L 1 spaces and their representing matrices », Acta Math.126 (1971), p. 165–193. Zbl0209.43201MR291771
  4. [4] J. Lindenstrauss, G. H. Olsen & Y. Sternfeld – « The Poulsen simplex », Ann. Inst. Fourier (Grenoble) 28 (1978), p. 91–114. Zbl0363.46006MR500918
  5. [5] Y. Sternfeld – « Characterization of Bauer simplices and some other classes of Choquet simplices by their representing matrices », in Notes in Banach spaces, Univ. Texas Press, 1980, p. 306–358. Zbl0556.46006MR606224

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