A generalization of Naundorf's fixpoint theorem

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Given is an ordered set in which every chain has an upper bound and every pair of elements has a greatest lower bound. Let Z be its set of maximal elements and let F be a function from Z to Z. A condition is presented that implies that F has a unique fixpoint. This is a generalization of a theorem of Naundorf. In Naundorf's theorem, the condition is related to causality for behaviour that develops in time. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)291-296
Number of pages6
JournalTheoretical Computer Science
Issue number1-2
Publication statusPublished - 28-Sep-2000


  • fixpoint theorem
  • semilattice
  • Zorns lemma
  • strict causality

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