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Fixed points of contractive maps on dcpo's

Published online by Cambridge University Press:  13 May 2013

E. COLEBUNDERS ,
S. DE WACHTER  and
R. LOWEN
E. COLEBUNDERS
Affiliation:
Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium Email: evacoleb@vub.ac.be; sdewacht@vub.ac.be
S. DE WACHTER
Affiliation:
Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium Email: evacoleb@vub.ac.be; sdewacht@vub.ac.be
R. LOWEN
Affiliation:
Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimlaan 1, 2020 Antwerpen, Belgium Email: bob.lowen@ua.ac.be
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 1 , February 2014 , e240102
Copyright
Copyright © Cambridge University Press 2013 

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