Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T12:07:16.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonclosed simplices and quasi-simplices

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

René Fourneau
René Fourneau
Affiliation:
Institut de Mathématique, Université de Liège, 15, avenue des Tilleuls, B-4000, Liège
Get access

Extract

A quasi-simplex of ℝd is the closure of a Choquet simplex of ℝd. We characterize these quasi-simplices and we use this characterization to describe the line-free Choquet simplices of ℝd.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 71 - 85
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bair, J and Fourneau, R.. Étude géométrique des espaces vectoriels-Une introduction, Lecture notes in Math.,489 (Springer-Verlag, Berlin-Heidelberg-New York, 1973).Google Scholar
2.Bair, J and Fourneau, R..Google Scholar
3.Bair, J. and Fourneau, R.Google Scholar
4.Bair, J and Fourneau, R.. “Caractérisation de polyèdres convexes et systèmes d'inéquations linéaires”, Bull. Soc. Roy. Sc. Liège, 45 (1976), 175–182.Google Scholar
5.Choquet, G. “Existence et unicité des représentations intégrates dans les cônes convexes”, C.R. Acad. Sc. Paris, 243 (1956), 555–557, 699–702, 736–737.Google Scholar
6.Fourneau, R.Google Scholar
7.Goullet de Rugy, A. Géométrie des simplexes (Centre de Documentation Universitaire, Paris, 1968).Google Scholar
8.Rogers, C.A and Shephard, G. C.. “The difference body of a Convex Body”, Archiv. Math., 8 (1957), 220–233,.CrossRefGoogle Scholar
9.Rockafellar, R.T. Convex Analysis (Princeton University Press, 1970).CrossRefGoogle Scholar
10.Simons, S. “Noncompact simplices”, Trans. Am. Math. Soc., 149 (1970), 155–161.CrossRefGoogle Scholar