## Comparison of convex hulls and box hulls.(English)Zbl 1157.52304

A convex hull of a set of points $$X$$ is the minimal convex set containing $$X$$. A box is a set of the form $$B=\{\vec x\in \mathbb{R}^d \mid \vec a \leq \vec x \leq \vec b\}$$ where $$\vec a$$ and $$\vec b$$ are vectors in $$\mathbb{R}^d$$ and the inequalities hold component-wise. A box hull of set of points $$X$$ is the minimal box containing $$X$$.
The paper describes several Helly-type theorems for box hulls.

### MSC:

 52A35 Helly-type theorems and geometric transversal theory 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces)

### Keywords:

convex hull; convex box; Helly-type theorems