The Cauchy completion of a symmetric b-uniform filter space

Abstract

b-uniform filter spaces are an appropriate tool for studying convergence from a higher point of view as demonstrated in two papers by the above mentioned authors. Fundamental properties of spaces in topology such as completeness, precompactness or compactness, respectively, can be newly defined and studied in the realm of these proper constructs. Moreover, we present a kind of completion, called Cauchy completion, which generalizes the corresponding concepts that arose in the past like the simple completion of semi-uniform convergence spaces in the sense of [10], the Wyler completion of separated uniform limit spaces [15], the Hausdorff completion of separated uniform spaces or the λ-completion of filter spaces in the sense of [2], and, last not least, the compactification of proximity spaces ([4], or [12], respectively).