Subject: categories: Papers on Lawvere's generalized metric spaces

From: Steve Vickers <[email-masked]>
Date: Mon, 08 Mar 2004 16:09:04 +0000

I have just put on the web two papers that explore constructive localic
(and also topos) aspects of Lawvere's generalized metric spaces (see TAC
Reprints 1, "Metric spaces, generalized logic and closed categories").
My papers are:

   "Localic completion of generalized metric spaces I"
   "Localic completion of generalized metric spaces II: Powerlocales"

They can both be found through

   http://www.cs.bham.ac.uk/~sjv/README.html

Lawvere describes generalized metric spaces as categories enriched over
the extended half line [0, infinity]. I replace this enrichment category
by a locale with the same points, and show how to obtain a completion as
a locale. Topos aspects include a proof that the generic localic
completion is an opfibration in the 2-category of grothendieck toposes.

My second paper shows how the powerlocales of the localic completions
are themselves also localic completions, and uses this to analyse
questions of compactness.

Steve Vickers.