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Fixed points of contractive maps on dcpo's

  • E. COLEBUNDERS (a1), S. DE WACHTER (a1) and R. LOWEN (a2)

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.

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Fixed points of contractive maps on dcpo's

  • E. COLEBUNDERS (a1), S. DE WACHTER (a1) and R. LOWEN (a2)

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