ELEMENTS OF GENERALIZED ULTRAMETRIC DOMAIN THEORY

Generalized ultrametric spaces are a common generalization of preorder s and ordinary ultrametric spaces, as was observed by Lawvere (1973). Guided by his enriched-categorical view on (ultra)metric spaces, we ge neralize the standard notions of Cauchy sequence and limit in an (ultr a)metric space, and of adjoint pair between preorders. This leads to a solution method for recursive domain equations that combines and exte nds the standard order-theoretic (Smyth and Plotkin, 1982) and metric (America and Rutten, 1989) approaches.