TITLE: A domain-theoretic metrization theorem
ABSTRACT: Classically, domains in the sense of Scott are used as models in
the Semantics of Programming Languages. Over the last forty years domain
theory has been used in a variety of other applications. During the talk
we will explain how domains can serve as models of topological spaces. In
particular, we will show how to give a necessary and sufficient condition
for a topology to be metrizable in the language of domain theory.
Concretely, the main theorem reads as follows: A topological space is
metrizable iff it is modelled as a kernel of a Lebesgue measurement on a
continuous poset. The result above appears in the doctoral thesis of K.
Martin and its original proof relies heavily on one of the famous
metrization theorems. During the talk we will outline how to give a
different, elementary proof (in fact - a construction) based only on
domain-theoretic methods. As a consequence, we gain a new understanding of
the nature of classical metrization theorems from the past century. Our
work is inspired by research of K.Martin, H-P. Kunzi and V. Vajner and
relies on some results from the author's PhD thesis.