9 Aug
1993
9 Aug
'93
3:58 p.m.
There is a well-known cartesian closed category of topological spaces, described in Mac Lane's CWM. A Hausdorff space is compactly generated if a set is closed iff its intersection with every compact subspace is closed. Question: does this construction generalize to an arbitrary topos? In other words is there a notion of compactly generated locale, such that we get a cartesian closed full subcategory of the category of locales over that topos? Ideally all separation axioms should be dropped. Also one would (well I would) like to have these locales to have enough points. Francois Lamarche, Imperial College. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++