Generalized Ultrametric Spaces

[-------The Types Forum---------http://www.dcs.gla.ac.uk/~types-------]
The following technical report is now
available at ftp.cwi.nl as pub/CWIreports/AP/CS-R9560.ps.Z.

Generalized Ultrametric Spaces:
Completion, Topology, and Powerdomains
via the Yoneda Embedding,
by M.M. Bonsangue, F. van Breugel, and J.J.M.M. Rutten.

Generalized ultrametric spaces are a common generalization
of preorders and ordinary ultrametric spaces (Lawvere
1973, Rutten 1995).
Combining Lawvere's (1973) enriched-categorical
and Smyth' (1987, 1991) topological view on generalized
(ultra)metric spaces, it is shown how to construct
1. completion, 2. topology, and 3. powerdomains
for generalized ultrametric spaces.
Restricted to the
special cases of preorders and ordinary ultrametric 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 powerdomain of compact subsets.
Interestingly, all constructions are formulated in terms
of (an ultrametric version of) the Yoneda (1954) lemma.