Which book (on topology) gives the most complete, yet accessible, account of the Hausdorff metric? the fuzzy metric? the cone metric? the probablistic metric? and so on?
Somebody once gave me a photocopy of a few pages containing a discussion of the Hausdorff metric; it was probably chapter 10 of some book, and it developed the Hausdorff metric axiomatically and derived its properties in a systematic fashion, but he doesn't remember where he took those pages, nor was the title mentioned in the header or the footer.
And what about such other metric spaces, like the cone metric spaces, the fuzzy metric space, and the probablistic metric spaces? I've looked up several books on topology, including Munkres, Simmons, and Lipschitz, but haven't found a discussion of these matters; Kelly gives an account of the Hausdorff metric but only in the exercises.
I have also checked E. T. Copson text on metric spaces and Walter Rudin and Apostol's texts on mathematical analysis. And, as far as I can remember, H. L. Royden doesn't cover these topics either.