Re: Uniformity via Cauchy filters?

Jeff Egger wrote in part:

one could define a uniform locale as a locale equipped with a designated set of Cauchy filters

This can be done, although you get a more general notion: a _Cauchy_space_ (or locale, but spaces have a bigger literature). Note that a uniform space is a Cauchy space with extra ~structure~; there is no way, in a mere Cauchy space, to compare sizes of neighbourhoods of different points. For the basic definition, you could do worse than the English Wikipedia: < http://en.wikipedia.org/wiki/Cauchy_space >. I had some references (monographs) that I liked too, but I can't find them now; perhaps I can find them tomorrow. --Toby