Hi Jeff, I don't know about locales, but I worked on issues surrounding taking a uniform space, and forgetting the uniformity but keeping the set of cauchy filters. This turns out to be a nontrivial amount of forgetting. I liked the result because the resulting category, which I call the category of completable spaces, can be used as a base category and, for example, if you have a commutative ring, you can look at the compatible completabilities on it (making it a completable space with the discrete completability) and they generalize the valuations on a field. Bill Rowan On Sun, 10 Feb 2008, Jeff Egger wrote:
Dear categorists,
One of my current research projects has drifted into the realm of uniform locales, which is not exactly my forte. As I went to re-familiarise myself with the assorted definitions, I found myself wondering whether one could define a uniform locale as a locale equipped with a designated set of Cauchy filters, instead of uniform covers, or entourages. Does anyone know whether this idea has already been pursued, either for locales or for spaces?
Cheers, Jeff.
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