Stone Duality for Stably Compact Spaces
by
Achim Jung
School of Computer Science, University of Birmingham, England
Coauthors: M. Andrew Moshier (Chapman University, Orange, California), Mathias Kegelmann (Technical University Darmstadt, Germany)

Over recent years, stably compact spaces have been identified as embodying the topological essence of semantic domains. In this talk I will explain this statement and then move on to various characterisations of stably compact spaces. The one which has intrigued us for some time is a direct generalisation of Stone's original duality for Boolean Algebras. In the same way as Boolean Algebras are related to Propositional Logic, so here, too, we get a logic from our variant of Stone Duality. The Logic is interesting in itself but may furthermore be seen as the backbone of logics for proofing properties of computer programs. In this sense, our work is an extension of Abramsky's "Domain Theory in Logical Form".

Date received: April 15, 2002