Partial metrics in lattice ordered abelian groups
by
Ralph Kopperman
City College of CUNY
Coauthors: M. Henriksen, Harvey Mudd College and H. Pajoohesh, UCC Cork

Partial metrics were introduced to study partial computations, which are incompletely defined and therefore have strictly positive self-distance.

However, they have many other uses; in this talk, we say that a topology on a lattice ordered group is Euclidean if (like the usual topology on the reals) it is a group topology, the lattice operations are continuous, and it has a base of order-convex sets.

Then, like the usual topology on the reals, it is the join of the topology of its upper open sets and that of its lower open sets, and the lattice order join is a partial metric that gives rise to all three of these topologies.

Date received: June 20, 2004