Abstract
Taking ordered monoids, which obey some extra axioms that concern the relation-ship between order relation and monoid structure we topologize them by means of the order relation and investigate the resulting spaces. They turn out to be fixpoint-spaces.
Proceeding to function spaces in which the elements are not only monoid operable, that means they can be added, but also structurable, that means components of elements can be selected and compound elements can be contructed from simpler ones, the axiomatic properties of the original spaces turn over to the latter ones; the algebraic operations are continous and thus fixpoint-equations with these operations can be solved.
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Literaturangaben
Ehrich, H.-D.: Outline of an algebraic theory of structured objects. Proc. 3rd International Colloquium on Automata, Languages, and Programming, Edingburgh University Press, Edinburgh 1976.
Indermark, K.: Gleichungsdefinierbarkeit in Relationalstrukturen, Bericht Nr. 98, Gesellschaft für Mathematik und Datenverarbeitung, 1975.
Loeckx, J.: The fixpoint-theorem and the Principle of Computational Induction. Bericht A 74/08 Universität Saarbrücken, Fachbereich Informatik, 1974.
Lohberger, V.: Axioms for Ordered Monoids that are Fixpoint-Spaces According to a suitable Topology. TR 28/76 Abteilung Informatik, Universität Dortmund, July 1976.
Lohberger, V.: Spaces of Structured Objects and Applications to the Semantics of Data Structures. TR 36/76 Abteilung Informatik, Universität Dortmund, in Prep.
Scott, D.: Continous Lattices. In: Topology, algebraic Geometry and Logic. Lecture Notes in Mathematics, Nr. 274. Springer, Berlin 1972.
Scott, D.: Data Types and Lattices. In: Müller, G.H. (ed): Proceedings of the International Summer Institute and Logic Colloquium, Kiel 1974, Springer Lecture Notes 499, Berlin 1975.
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Lohberger, V. (1977). Eine Klasse geordneter Monoide und ihre Anwendbarkeit in der Fixpunktsemantik. In: Theoretical Computer Science. Lecture Notes in Computer Science, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08138-0_15
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DOI: https://doi.org/10.1007/3-540-08138-0_15
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Online ISBN: 978-3-540-37389-6
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