A theory of description
by
Keye Martin
Tulane University

A model of a space X is a continuous dcpo D (directed complete partial order) together with a homeomorphism from X onto the maximal elements of D, which are a space in their relative Scott topology -- an intrinsic topology defined by the order on any partially ordered set. Question: Which spaces may be realized as the maximal elements of a domain (continuous dpco) ?

Much progress has been made on this question recently; for example, a regular space may be realized as the set of maximal elements of a countably based domain iff it is a Polish space. But why can we prove such theorems? This talk identifies an essential topological property possessed by maximal elements that serves to explain their curious behavior. The observations made in this talk should give researchers in the area a new perspective on the problem, as well as attract topologists from outside of domain theory and theoretical computation.

Date received: June 23, 1999