Dear Comprox and Categories members, Here is a short note that Reinhold Heckmann and I have written. Your comments are welcome, as always. On function spaces in topology ------------------------------ It is the purpose of this expository note to provide a self-contained, elementary and brief development of the fact that the exponentiable topological spaces are precisely the core-compact spaces. The only prerequisite is a basic knowledge of topology (continuous functions, product topology and compactness). We hope that teachers and students of topology will find this useful. As far as we know, there is no such development available in the literature. Although there are one or two embellishments, our methods are certainly not original. We briefly discuss more advanced treatments in the introduction. ------------------------------------------------------------------- http://www.dcs.st-and.ac.uk/~mhe/papers/exponentiablespaces.ps.gz http://www.dcs.st-and.ac.uk/~mhe/papers/exponentiablespaces.dvi.gz http://www.dcs.st-and.ac.uk/~mhe/papers/exponentiablespaces.ps http://www.dcs.st-and.ac.uk/~mhe/papers/exponentiablespaces.dvi ------------------------------------------------------------------- Best regards, Martin & Reinhold