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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
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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

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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