Descriptive properties of the set of exposed points of compact convex sets in $\mathbb {R}^3$
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- by Petr Holický and Miklós Laczkovich PDF
- Proc. Amer. Math. Soc. 132 (2004), 3345-3347 Request permission
Abstract:
We construct a compact convex subset of $\mathbb R^3$ such that the set of its exposed points is not the intersection of an $F_{\sigma }$ set and a $G_{\delta }$ set. The existence of such a set answers a question posed by G. Choquet, H.H. Corson and V.L. Klee.References
- Gustave Choquet, Harry Corson, and Victor Klee, Exposed points of convex sets, Pacific J. Math. 17 (1966), 33–43. MR 198176
- H. H. Corson, A compact convex set in $E^{3}$ whose exposed points are of the first category, Proc. Amer. Math. Soc. 16 (1965), 1015–1021. MR 180917, DOI 10.1090/S0002-9939-1965-0180917-5
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
Additional Information
- Petr Holický
- Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 95 Prague 8, Czech Republic
- Email: holicky@karlin.mff.cuni.cz
- Miklós Laczkovich
- Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/c, Hungary – and – Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England
- Email: laczk@cs.elte.hu
- Received by editor(s): February 5, 2003
- Received by editor(s) in revised form: July 21, 2003
- Published electronically: April 21, 2004
- Additional Notes: The first author was supported by the “Mathematics in Information Society” project carried out by Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, in the framework of the European Community’s “Confirming the International Role of Community Research” program. The research was partly supported also by grants GAČR 201/03/0931 and MSM 113200007
The second author was partially supported by the Hungarian National Foundation for Scientific Research Grant No. T032042 - Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3345-3347
- MSC (2000): Primary 52A15, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-04-07445-3
- MathSciNet review: 2073311