Tag Archives: quasi-uniform space

Quasi-uniform spaces IV: Formal balls—a proposal

Posted on January 23, 2021 by jgl

Formal balls are an extraordinarily useful notion in the study of quasi-metric, and even hemi-metric spaces. Is there any way of extending the notion to the case of quasi-uniform spaces? This is what I would like to start investigating. This … Continue reading →

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Quasi-uniform spaces III: Smyth-completeness, symcompactness

Posted on December 20, 2020 by jgl

We embark on the study of notions of completeness for quasi-uniform spaces, and we concentrate on Smyth-completeness. We will see that at least two familiar theorems from the realm of quasi-metric spaces generalize to quasi-uniform spaces: all Smyth-complete quasi-uniform spaces … Continue reading →

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Quasi-uniform spaces II: Stably compact spaces

Posted on November 21, 2020 by jgl

There is a standard result in the theory of uniform spaces that shows (again) how magical compact Hausdorff space can be: for every compact Hausdorff space X, there is a unique uniformity that induces the topology of X, and its … Continue reading →

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Quasi-Uniform Spaces I: Pervin Quasi-Uniformities, Pervin Spaces

Posted on October 19, 2020 by jgl

A uniform space is a natural generalization of the notion of a metric space, on which completeness still makes sense. It is rather puzzling that I managed to avoid the subject of quasi-uniform spaces in something like the 7 years … Continue reading →

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