Fixed points of contractive maps on DCPO's

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

Publication year:2014

Keywords:dcpo, weightable quasi metric, approach space, Scott topology, fixed point

CSS-citation score:1

Accessibility:Open