A unified functional look at completion in MET, UNIF and AP (Q1840748)

A description is given of the completion of metric spaces in which the points of the completion space are a certain type of map, referred to as ``supertight.'' By appropriate modifications this method yields completions of both Hausdorff uniform and Hausdorff uniform approach spaces. From this, alternative characterizations of metric, uniform, and uniform approach completeness follows. The paper concludes by showing, in these cases, how morphisms into complete Hausdorff objects can be extended to the completion of their domain.