Encounters Between Topology and Domain Theory

Abstract

This survey article provides an overview of recent developments that represent typical interplays between topology and continuous domain theory. The topics highlighted include locally compact spaces, spectral theory, round-ideal completions, ordered spaces, maximal-point spaces, and the probabilistic power domain The article attempts to develop the thesis that topological tools are useful for the investigation of order-theoretic structures arising in theoretical computer science and the latter in turn suggest new research directions in topology.