Information Systems for Continuous Posets

The method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive. This develops results of Raney on completely distributive lattices and of Hoofman on continuous Scott domains, and also generalizes Smyth’s “R-structures”. Various constructions on continuous posets have neat descriptions in terms of these continuous information systems; here we describe Hoffmann-Lawson duality (which could not be done easily with R-structures) and Vietoris power locales.