[------ The Types Forum ------- http://www.dcs.gla.ac.uk/~types ------]
I would be much obliged if the following
announcement could be distributed among the members
of your list.
Yours, Jan Rutten
The following technical report is now
available at ftp.cwi.nl as pub/CWIreports/AP/CS-R9636.ps.Z
(also via http://www.cwi.nl/~janr). It generalizes
the results of an earlier report (CS-R9560) with almost
the same title, which was on ultrametric spaces.
Technical Report CS-R9636, CWI, Amsterdam, 1996.
Generalized Metric Spaces:
Completion, Topology, and Powerdomains
via the Yoneda Embedding,
by: M.M. Bonsangue, F. van Breugel, J.J.M.M. Rutten.
Generalized metric spaces are a common generalization
of preorders and ordinary metric spaces (Lawvere
Combining Lawvere's (1973) enriched-categorical
and Smyth' (1988, 1991) topological view on generalized
metric spaces, it is shown how to construct
1. completion, 2. topology, and 3. powerdomains
for generalized metric spaces.
Restricted to the
special cases of preorders and ordinary metric spaces,
these constructions yield, respectively:
1. chain completion and Cauchy completion;
2. the Alexandroff and the Scott topology, and
the epsilon-ball topology;
3. lower, upper, and convex powerdomains,
and the hyperspace of compact subsets.
All constructions are formulated in terms
of (a metric version of) the Yoneda (1954) embedding.