Vaughan points out that Wilson space didn't make it into the index of Cats & Allegators. Whoops. It's to be found in section 1.749, page 129 (but not in small caps, which, I guess, is how it was missed when preparing the index). It is not an order-interval topology. Indeed, it is not Hausdorf. As I remarked in my last post, Wilson space is definable as the final co-algebra of the functor on Top that sends X to the scone of X + X. (The only Hausdorf scone is the scone of the empty set.) Its important properties are two: 1) the category of sheaves on Wilson space is equivalent to the category of pre-sheaves on the infinite binary tree (viewed as a poset with the root as top); and, 2) there's an open continuous map from the closed interval onto Wilson space (hence from any reasonable locally euclidean space). All of which yields a completeness theorem for intuitionistic first-order logic with respect to the semantics of sheaves on the reals (or any reasonable locally euclidean space). 29-Nov-2004 11:21:44 -0400,6038;000000000000-00000000