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A unified functional look at completion in MET, UNIF and AP. (English) Zbl 0987.54021

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.

MSC:

54B30 Categorical methods in general topology
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54E15 Uniform structures and generalizations
54E35 Metric spaces, metrizability
54E99 Topological spaces with richer structures
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