Centre of a compact convex set

On the Chvátal-Gomory Closure of a Compact Convex Set

In this paper, we show that the Chvátal-Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver [17] for irrational polytopes1, and generalizes the same result for the case of rational polytopes [17], rational ellipsoids [8] and strictly convex bodies [7].

A short proof for the polyhedrality of the Chvátal-Gomory closure of a compact convex set

Recently Schrijver’s open problem, whether the Chvátal-Gomory closure of an irrational polytope is polyhedral was answered independently in the seminal works of Dadush et al. [2011] and Dunkel and Schulz [2010]; the former even applies to general compact convex sets. We present a very short, easily accessible proof.

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

A Compact Convex Set in £3 Whose Exposed Points Are of the First Category

Subdivision Schemes for Non-convex Compact Sets with a New Definition of Set Average

Set valued functions possess a lot of application future. In this paper we improve the definition of set average defined in Artstein [1]. Based on the new definition the spline subdivision schemes as well as the interpolatory subdivision schemes for general compact sets are introduced. Furthermore the convergence properties of the subdivision schemes are discussed. Comparison results based on t...