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Description: |
Much work has been done on porting the theory of uniform spaces to the pointfree context and uniform frames/locales have proved to be a useful tool in this setting. However, much of the utility of the pointfree approach lies in its constructive theory. Formulating topological results constructively yields as corollaries, not only the standard classical results, but also analogous results in fibrewise, equivariant and computable topology. Unfortunately, aside from a short paper by Johnstone, the constructive theory of uniform locales has been left undeveloped. I will discuss the first steps in the development of this theory. Also of interest to classical mathematicians might be the discussion of pre-uniform locales and my approach to entourage uniformities.
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