On duality and endomorphisms of lattices of closed convex sets

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء


The class of closed convex sets in ℝn is a lattice with respect to the operations of intersections and closed convex hulls of unions. We completely classify the endomorphisms of this lattice and its sublattice consisting of sets containing the origin 0. We show that they consist of constant maps and maps induced by the affine group. As a consequence, we obtain a characterization of the duality mapping for the class of closed convex sets containing 0. Moreover, by modifying a proof of Böröczky and Schneider we obtain the same result for the sublattice consisting of compact bodies containing 0.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)225-239
عدد الصفحات15
دوريةAdvances in Geometry
مستوى الصوت11
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - أبريل 2011
منشور خارجيًانعم

ملاحظة ببليوغرافية

Funding Information:
∗This paper is part of the author’s M.Sc thesis, prepared under the supervision of Prof. Shiri Artstein-Avidan. The research was partially supported by ISF grant No. 865/07.


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