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arXiv · 2207.11973

Blaschke and Separation Theorems for Orthogonally Convex Sets

Phan Thanh An·Nguyen Thi Le
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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.

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Phan Thanh An, Nguyen Thi Le. 2022-07-25. Blaschke and Separation Theorems for Orthogonally Convex Sets. https://doi.org/10.1007/s10957-026-03041-y

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