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 entourages are exactly the neighborhoods of the diagonal. How can we generalize this to stably compact spaces? No, the topology of a stably compact space is not induced by a unique quasi-uniformity… the result has to be a bit more subtle than that. In passing, we will see that every core-compact space, and in particular every locally compact space, has a minimal compatible quasi-uniformity, which has a very simple description. Read the full post.

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