Generalized metric topologies on lattice ordered groups
Time and place
4 PM on Thursday, October 18th, 2007; CCNY, NAC 4/205
Homeira Pajoohesh (Medgar Evers College, CUNY)
Abstract
"Intrinsic" metrics into lattice ordered groups have long been considered. Topologies on such groups have been considered as well. But topologies often arise from metrics into the reals, and getting topologies from these metrics into lattice ordered groups has not been discussed. A key issue must be overcome: properties of the strictly positive reals key to defining the metric topology fail for the strictly positive elements of a typical lattice ordered group. We solve this problem, and show how some important topologies indeed arise from metrics.
We define partial metrics and discuss their uses in computer science, in obtaining intrinsic topologies on lattice ordered groups, and elsewhere. A central use for them is to split certain metric topologies on ordered sets, into upper and lower subtopologies. Among these is the Euclidean topology on the lattice ordered group of real numbers.
