Research Interests: I work in locale theory and topos theory. My preoccupation is that the theory of compact Hausdorff spaces and the theory of sets have such a lot in common that they can be expressed as the same theory. Therefore I am developing axioms for a category of spaces in which the theory of compact Hausdorff spaces is dual to the theory of sets (the duality is not standard categorical duality, but is order enriched duality; the category of spaces is order enriched). A further aim is to extend this work to an axiomatization of the category of Grothendieck toposes.
For a draft English translation of parts 0-4, 'Lecture IV', SGA4 click here