Face relative interior of convex sets in topological vector spaces

2023/09/13 by Reinier Díaz Mill án, án, Reinier Díaz Mill, Vera Roshchina +1
Computer Science · #FOS: Mathematics #General Topology (math.GN) #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2309.06699

openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new notion of face relative interior for convex sets in topological real vector spaces is introduced in this work. Face relative interior is grounded in the facial structure, and may capture the geometry of convex sets in topological vector spaces better than other generalisations of relative interior. We show that the face relative interior partitions convex sets into face relative interiors of their closure-equivalent faces (different to the partition generated by intrinsic cores), establish the conditions for nonemptiness of this new notion, compare the face relative interior with other concepts of convex interior and prove basic calculus rules.

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