if we have an (abelian, say) topological group, there is a natural uniform topology on the group such that the operations are uniformly continuous. Does the same hold for abelian group objects in the category of Kelley spaces?
As others have already noted, the answer is no. One possible solution (assuming you regard this as a defect) is to apply the idea implicit in the definition of Kelley space, not to the category of all topological spaces, but to that of all Tychonov (=uniformisable) spaces. What results is a cartesian closed category (that of "k_R-Tychonov spaces") with somewhat different properties; a group in this category is tautologously uniformisable and, if I recall correctly, is also true that the operations are uniformly continuous. Gabor Lukacs has studied these things and spoken about them at several conferences. Cheers, Jeff. __________________________________________________________________ Yahoo! Canada Toolbar: Search from anywhere on the web, and bookmark your favourite sites. Download it now at http://ca.toolbar.yahoo.com.