Complete sets and completion of sets in Banach spaces
Horst Martini, Pier Luigi Papini, and Margarita Spirova
TL;DR
This paper investigates the properties of complete sets and their completions in Banach spaces, focusing on the relationships between diameters, radii, and centers, supported by various examples.
Contribution
It provides new insights into the structure and size of completions of sets in Banach spaces, including detailed relationships among geometric properties.
Findings
Analysis of the size and structure of set completions
Relationships between diameters, radii, and centers in Banach spaces
Illustrative examples demonstrating theoretical results
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.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Fixed Point Theorems Analysis