Pointed Closed Convex Sets are the Intersection of All Rational Supporting Closed Halfspaces

2018/02/08 by Marcel K. de Carli Silva, Silva, Marcel K. de Carli, Levent Tunçel +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #FOS: Mathematics #Limits and Structures in Graph Theory #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1802.03296

openalex publication_date 2018/02/08 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28

Abstract

We prove that every pointed closed convex set in ℝⁿ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.

Related

• Complements of rationally convex sets
• On the boundary of closed convex sets in Eⁿ
• On the Chvatal-Gomory Closure of a Compact Convex Set
• Non-Convexity
• Intersection Theorems for Closed Convex Sets and Applications