Fixed Points and Reflexive Domain Equations in Categories of Continuity Spaces

Abstract

This paper continues the study of the general theory, begun in [4], of semantic domains based on the notion of a symmetrically compact ν-continuity space, where ν is a value quantale. It was previously shown that this theory naturally includes the traditional examples of domains of cpo's and metric spaces, is closed under the key type forming operations needed in denotational semantics, and provides new examples which may be suitable for modeling language constructs that occur in concurrent and probabilistic programming. Here it is shown that ν-Dom supports a rich theory of fixed points for morphisms and has solutions to a wide class of reflexive domain equations.