Complete sets and completion of sets in Banach spaces

2013/08/04 by Horst Martini, Martini, Horst, Pier Luigi Papini +3
Computer Science · Mathematics · #46B20 #46B99 #52A05 #52A20 #52A21 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1308.0789

openalex publication_date 2013/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and centers. The results are illustrated by several examples.

Related

• Uniqueness of completions and related topics
• New examples of complete sets, with connections to a Diophantine theorem of Furstenberg
• A generic approach to measuring the strength of completeness/compactness\n of various types of spaces and ordered structures
• On Metric Completness and Completness in sense of Lattices
• Decomposition of the set of Banach limits into discrete and continuous subsets