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 on X ; and a collection of weights corresponding to the quasi metrics. Understanding the interaction between these structures on X will 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.