A Krasnosel'skii-type theorem for an enlarged class of orthogonal polytopes

作者：Breen Marilyn^*

来源：Advances in Geometry, 2017, 17(4): 525-532.

DOI：10.1515/advgeom-2017-0031

• Orthogonal polygon
• staircase convex set
• staircase starshaped set
• median space

Let C be a finite family of distinct boxes in R-d, let S =boolean OR{C : C in C} and let G be the intersection graph of C. For each block of G, assume that the corresponding members of C have a staircase convex union. Then S with the rectilinear metric is a median space. Moreover, if every two points of S see a common point via staircase paths in S, then S is staircase starshaped.

• 出版日期2017-10