Hi. Does anyone know if the following perspective on topology has been studied before (and if so, is there a good reference)? Apologies if I'm missing something very basic here. Let T_0 be the category of T_0 topological spaces and continuous homomorphisms. We have the usual functor (T_0)^op ---> Coframe (this is all 1-dimensional, so you can call it Frame if you prefer) sending a topological space to the coframe of closed sets. This is a faithful fibration. (It can be extended to arbitrary topological spaces, but isn't faithful.) Furthermore, all the non-empty fibres are posets with top elements. These top elements are the sober spaces, and the restriction of the functor to them is full and has an adjoint, which is the usual equivalence between sober spaces and spatial locales. On the other hand, for a large class of coframes (coframes in which every element is a sup of elements which are not _equal_ to the sup of a set of strictly smaller elements), the fibres are complete boolean algebras. Thus the fibres have bottom elements. These are topological spaces where for any point x, x is open in the subspace topology on its closure. Since these spaces are at the bottom of the boolean algebra with sober spaces at the top, they should presumably be called "drunk spaces", though this does lead to there being a large class of spaces which are both sober and drunk. All T_1 spaces are drunk. When restricted to drunk spaces, the functor is not full. However, its image is a subcategory of Coframe (I think the morphisms in the image are complete co-Heyting homomorphisms). When we restrict to this subcategory, we get an equivalence between drunk topological spaces and completely indecomposable-generated coframes with complete co-Heyting algebra homomorphisms. Does anyone know if this duality between "drunk" spaces and indecomposably-generated coframes has been studied? The motivation here is that the fibration extends to a fibration from closure spaces to Inf-lattices, and the usual top element adjoint in this extension is not very interesting, and is on the wrong side for my purposes, but the restricted equivalence above looks like it covers more of the cases of interest. Regards, Toby Kenney [For admin and other information see: http://www.mta.ca/~cat-dist/ ]