On the uniqueness of fixed points endofunctors in a category of complete metric spaces

Majster-Cederbaum, Mila

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URL: https://ub-madoc.bib.uni-mannheim.de/1865
URN: urn:nbn:de:bsz:180-madoc-18651
Document Type: Working paper
Year of publication: 1988
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: 54B30 68Q55 54H25 54E50 ,
Subject headings (SWD): Nebenläufigkeit , Synchronisierung , Festkommarechnung , Kompakter metrischer Raum , Kontraktion <Mathematik>
Keywords (English): concurrency , synchronisation , fixed point equations , complete metric spaces , contractiveness
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. Recently, the question under which circumstances fixed point equations involving complete metric spaces can be (unsquely) solved has attracted attention, e.g. [1,10]. In [1], a criterion for the existence of a solution, namely the contractiveness of the respectitve functor, is provided. Contractiveness together with an addtional criterton, the hom-contractiveness was shown in [1] to guarantee uniqueness. The problem of uniqueness is the topic of our contribution.
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