Fixed points of contractive maps on dcpo's

Abstract

In this paper we study approach structures on dcpo's. A dcpo (X, ≤) will be endowed with several other structures: the Scott topology; an approach structure generated by a collection of weightable quasi metrics onX; and a collectionof weights corresponding to the quasi metrics. Understanding the interaction between these structures onXwill eventually lead to some fixed-point theorems for the morphisms in the category of approach spaces, which are called contractions. Existing fixed-point theorems on both monotone and non-monotone maps are obtained as special cases.