On the Yoneda completion of a quasi-metric space
The authors consider two notions for the completion of rather general classes of topological spaces: the Yoneda completion of generalized metric spaces and the Smyth completion. (Such considerations are motivated in part by earlier efforts to reconcile continuous domain theory and metric space theory within a common framework.) A net-theoretic version of the Yoneda completion is given that complements the net-version of the Smyth completion and allows their comparison. The authors show further that the largest class of quasi-metric spaces idempotent under the Yoneda completion is precisely the class of Smyth-completable spaces. The preservation of various topological properties such as total boundedness, precompactness, compactness, and others under these completions is also considered.
scientific article; zbMATH DE number 1768079
scientific article