The contraction property is sufficient to guarantee the uniqueness of fixed points of endofunctors in a category of acomplete metric spaces

Majster-Cederbaum, Mila

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URN: urn:nbn:de:bsz:180-madoc-18667
Document Type: Working paper
Year of publication: 1989
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 68N25 54E35 54H25 68Q60 18B30 ,
Subject headings (SWD): Programmiersprache , Fixpunkt-Methode , Nebenläufigkeit , Kompakter metrischer Raum , Synchronisierung
Keywords (English): semantics of programming languages , fixed points of endofunctors , concurrency , synchronisation , complete metric spaces , contraction property
Abstract: In de Bakker and Zucker proposed to use complete metric spaces for the semantic definition of programming languages that allow for concurrency and synchronisation. The use of the tools of metric topology has been advocated by Nivat and his colleagues already in the seventies and metric topology was successfully applied to various problems (12, 13). Recently, the question under which circumstances fixed point equations involving complete metric spaces can be (uniquely) solved has attracted attention, e.g. (1,11). The solution of such equation provides the basis for the semantics of a given language and is hence of practical relevance. In (1), a criterion for the existence of a solution, namely that the respective functor is contracting, is provided. This property together with an additional criterion, namely that the respective functor is hom-contracting, was shown in (1) to guarantee uniqueness. In this paper we show that the contraction property is already sufficient to guarantee the uniqueness.
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