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 are quasi-sober, and the symcompact quasi-uniform spaces are exactly those that are Smyth-complete and totally bounded. However, and especially for the latter result, the proofs will be trickier. Read the full post.

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