A generalization of Naundorf's fixpoint theorem

Given is an ordered set in which every chain has an upper bound and every p air of elements has a greatest lower bound. Let Z be its set of maximal ele ments and let F be a function from Z to Z. A condition is presented that im plies that F has a unique fixpoint. This is a generalization of a theorem o f Naundorf. In Naundorf's theorem, the condition is related to causality fo r behaviour that develops in time. (C) 2000 Elsevier Science B.V. All right s reserved.