2018 Volume 72 Issue 2 Pages 239-252
Let Top and Diff be the categories of topological and diffeological spaces,respectively. By using an adjunction between Top and Diff we show that the full subcategory NG of Top consisting of numerically generated spaces is complete, cocomplete and cartesian closed. In fact, NG can be embedded into Diff as a cartesian closed full subcategory. It follows then that the category NG0 of numerically generated pointed spaces is complete,cocomplete and monoidally closed with respect to the smash product. These features of NG0 are used to establish a simple but flexible method for constructing generalized homology and cohomology theories by using the notion of enriched bifunctors.