Solutions of Functorial and Non-Functorial Metric Domain Equations

Abstract

A new method for solving domain equations in categories of metric spaces is studied. The categories CMS≈ and KMS≈ are introduced, having complete and compact metric spaces as objects and ɛ-adjoint pairs as arrows. The existence and uniqueness of fixed points for certain endofunctors on these categories is established. The classes of complete and compact metric spaces are considered as pseudo-metric spaces, and it is shown how to solve domain equations in a non-categorical framework.