TITLE: Stone Spaces, Locales, and Topoi for the (relative) beginner
QUESTION [7 upvotes]: I am currently reading Vickers' text "topology via logic" and Peter Johnstone's "stone spaces", and I understand the material in both of these texts to pertain directly to constructions in elementary topos theory (by which I do not mean 'the theory of elementary topoi). However, these things do not seem to be mentioned explicitly in these texts, at least not to great extent. Where might I avail myself of material which really 'brings home' the notion of topoi as 'generalized spaces' in the context of stone spaces and locales as alluded to in Vickers and Johnstone? I understand that Borceaux's third volume in the 'handbook of categorical algebra' is probably a good place to start...

REPLY [5 votes]: My article "Locales and toposes as spaces", in the Handbook of Spatial Logics, serves as a readers' guide to Mac Lane and Moerdijk to show how the results there can be used to create Grothendieck's concept of toposes as generalized spaces.