2023/01/05 by P. Bandyopadhyay, Deepak Gothwal, Bandyopadhyay, Pradipta +1
Computer Science · Mathematics · #46B20 #FOS: Mathematics #Functional Analysis (math.FA) #Limits and Structures in Graph Theory #Optimization and Search Problems #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2301.01974
openalex publication_date 2023/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a family C of closed bounded convex sets in a Banach space X, we say that X has the C-MIP if every C ∈ C is the intersection of the closed balls containing it. In this paper, we introduce a stronger version of the C-MIP and show that it is a more satisfactory generalisation of the MIP inasmuch as one can obtain complete analogues of various characterisations of the MIP. We also introduce uniform versions of the (strong) C-MIP and characterise them analogously. Even in this case, the strong C-UMIP appears to have richer characterisations than the C-UMIP.