A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
Marilyn Breen · Advances in Geometry · 2020
Abstract Let 𝒞 be a finite family of distinct axis-parallel boxes in ℝ d whose intersection graph is a tree, and let S = ⋃{C : C in 𝒞}. If every two points of S see a common point of S via k-staircase paths, then S is starshaped via k-staircase paths. Moreover, the k-staircase kernel of S will be convex via k-staircases.