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Duality on Convex Sets in Generalized Regions

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Asymptotic Geometric Analysis

Part of the book series: Fields Institute Communications ((FIC,volume 68))

Abstract

Recently, the duality relation on several families of convex sets was shown to be completely characterized by the simple property of reversing order. The families discussed in aforementioned results were convex sets in \({\mathbb{R}}^{n}\). Our goal in this note is to generalize this type of results to regions in \({\mathbb{R}}^{n}\) bounded between two convex sets.

Mathematical Subject Classifications (2010): 26B25, 06D50, 52A20

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Acknowledgements

The authors would like to thank Prof. Vitali Milman and Prof. Shiri Artstein for suggesting to consider this generalization of order isomorphisms for convex regions and their useful advice and comments. The first named author was partially supported by the ISF grant no. 387/09, and the second named author was partially supported by the ISF grant no. 247/11. The research is supported in part by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.

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Correspondence to Alexander Segal .

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Segal, A., Slomka, B.A. (2013). Duality on Convex Sets in Generalized Regions. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_13

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