On the quantification of uniform properties. Part 2

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact. Since then several variants and generalizations concerning quantification of topological and uniform properties have been studied. The introduction of approach uniform spaces, establishes a unifying setting which allows for a canonical quantification of uniform concepts, such as completeness, which is the subject of this article.