Blaschke and Separation Theorems for Orthogonally Convex Sets

Abstract

In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of these sets is established using suitable grids. Consequently, a closed and orthogonally convex set is represented by the intersection of staircase-halfplanes in the plane. Some topological properties of orthogonally convex sets in dimensional spaces are also given.

arXiv comment17 pages, 10 figures, adding more references, edit the title

References in corpus (1)

• Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations