Helly-type theorems for intersections of sets starshaped via orthogonally convex paths (Q1925804)

The author obtains Helly-type theorems in the framework provided by the replacement of the straight-line segment by the path that is orthogonally convex. The main result refers to a given family \(\mathcal{K}\) of simply connected sets in the plane. It states that if every subfamily of \(\mathcal{K}\) has a starshaped via orthogonally convex path intersection then the family \(\mathcal{K}\) itself has such an intersection. The particular \(d\)-dimensional and finite cases are discussed.