Partial convexity (Q5906909)

The aim of this paper is to study some questions related to the notion of partial convexity. Given a set \(V\subseteq \mathbb{R}^n\) of directions, a set \(X\subseteq \mathbb{R}^n\) is called \(V\)-convex or partially convex if the intersection of any line parallel to a vector in \(V\) with \(X\) is connected. This notion applies to the study of non convex geometric objects and can be useful in applications. In this paper the authors investigate the notions of semispaces and cones of convex directions with respect to partial convexity.