𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Separation of Plane Convex Sets

✍ Scribed by Eduardo Rivera-Campo; Jenö Töröcsik

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
77 KB
Volume
14
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

We show that in any family (F) of (n \geqslant 5) convex sets in the plane with pairwise disjoint relative interiors, there are two sets (A) and (B) such that every line that separates them, separates either (A) or (B) from at least ((n+28) / 30) sets in (F).

📜 SIMILAR VOLUMES

Centres of Convex Sets inLpMetrics
Centres of Convex Sets inLpMetrics
✍ Krzysztof Przesławski 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 397 KB

It is shown that for each convex body A/R n there exists a naturally defined family G A /C(S n&1 ) such that for every g # G A , and every convex function f : R Ä R the mapping y [ S n&1 f ( g(x)&( y, x)) d\_(x) has a minimizer which belongs to A. As an application, approximation of convex bodies by

Bounds for linear functionals on convex
Bounds for linear functionals on convex sets
✍ Walter Roth 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 187 KB

## Abstract We consider continuous monotone linear functionals on a locally convex ordered topological vector space that are sandwiched between a given \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(\mathbb R\cup \lbrace +\infty \rbrace )$\end{document}‐valued subline

On blocking sets of inversive planes
On blocking sets of inversive planes
✍ György Kiss; Stefano Marcugini; Fernanda Pambianco 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB

## Abstract Let __S__ be a blocking set in an inversive plane of order __q__. It was shown by Bruen and Rothschild 1 that |__S__| ≥ 2__q__ for __q__ ≥ 9. We prove that if __q__ is sufficiently large, __C__ is a fixed natural number and |__S__ = 2__q__ + __C__, then roughly 2/3 of the circles of the

Best Approximation on Convex Sets in Met
Best Approximation on Convex Sets in Metric Linear Spaces
✍ G. C. Ahuja; T. D. Narang; Swaran Trehan 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 256 KB

## Abstract In this paper the concepts of strictly convex and uniformly convex normed linear spaces are extended to metric linear spaces. A relationship between strict convexity and uniform convexity is established. Some existence and uniqueness theorems on best approximation in metric linear space