Strong restricted-orientation convexity
Traditional convex sets are defined by saying that any pair of points are ``straight segment'' visible. Strong \(O\)-convexity replaces segments by so called \(O\)-blocks. An orientation set \(O\) is a set of hyperplanes in \(R^d\) through a common point. Given \(H \in O\) denote \(H_p\) the hyperplane parallel to \(H\) that passes through \(p\). For two points \(p,q\) an \(O\)-block is the subset of \(R^d\) with the property that for every \(H \in O\) it is contained in between the pair of hyperplanes, \(H_p\),\(H_q\). For a set of hyperplanes a set is strongly \(O\)-convex if for every two points their \(O\)-block is contained in the set. The authors extend usual properties of intersection, supporting hyperplanes, etc. for this new generalized convexity.
scientific article; zbMATH DE number 1127653