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Quantitative Steinitz theorem: A spherical version
- Publication Year :
- 2023
-
Abstract
- Steinitz's theorem states that if the origin belongs to the interior of the convex hull of a set $Q \subset \mathbb{R}^d$, then there are at most $2d$ points $Q^\prime$ of $Q$ whose convex hull contains the origin in the interior. B\'ar\'any, Katchalski and Pach gave a quantitative version whereby the radius of the ball contained in the convex hull of $Q^\prime$ is bounded from below. In the present note, we show that a Euclidean result of this kind implies a corresponding spherical version.<br />Comment: Only minor corrections to the previous version
- Subjects :
- Mathematics - Metric Geometry
52A27 (primary), 52A35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.01663
- Document Type :
- Working Paper