In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.
Bibliographical noteFunding Information:
✩ The first and second named authors were partially supported by the ISF grant No. 387/09 and the third named author was partially supported by the ISF grant No. 865/07. * Corresponding author. Fax: +972 77 4220101. E-mail addresses: firstname.lastname@example.org (V.D. Milman), email@example.com (A. Segal), firstname.lastname@example.org, email@example.com (B.A. Slomka).
- Polar convex sets
- Section-projection correspondence