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Tag Archives: quasi-uniform space
Quasi-uniform spaces IV: Formal balls—a proposal
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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Tagged formal ball, quasi-uniform space
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Quasi-uniform spaces III: Smyth-completeness, symcompactness
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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Tagged completeness, quasi-uniform space
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Quasi-uniform spaces II: Stably compact spaces
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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Tagged quasi-uniform space, stably compact space
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Quasi-Uniform Spaces I: Pervin Quasi-Uniformities, Pervin Spaces
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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Tagged quasi-uniform space
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