More about cofinally complete metric spaces

TL;DR

This paper explores the properties of cofinally complete metric spaces, examining their relationship with almost uniformly continuous functions and providing equivalent conditions involving geometric functionals.

Contribution

It introduces new connections between cofinally complete metric spaces and almost uniformly continuous functions, with characterizations involving geometric functionals.

Findings

Established relationships between cofinally complete spaces and almost uniformly continuous functions

Provided equivalent conditions for spaces with cofinally complete completions

Enhanced understanding of the structure of cofinally complete metric spaces

Abstract

Metric spaces satisfying properties stronger than completeness and weaker than compactness have been studied by many authors over the years. One such significant family is that of cofinally complete metric spaces. We discuss the relationship between cofinally complete metric spaces and the family of almost uniformly continuous functions, which has recently been introduced by Kyriakos Keremedis in \cite{[K]}. We also discuss several equivalent conditions for metric spaces whose completions are cofinally complete in terms of some geometric functional.