  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.
