On the uniqueness of fixed points of endofunctors in a category of complete metric spaces (Q1114959)

\textit{J. W. De Bakker} and \textit{J. I. Zucker} [Inf. Control 54, 70-120 (1982; Zbl 0508.68011)] 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 (uniquely) solved has attracted attention [see, e.g., \textit{P. America} and \textit{J. Rutten}, Mathematical foundations of programming languages semantics, Proc. Workshop, New Orleans/LA 1987, Lect. Notes Comput. Sci. 298, 254-288 (1988)]. America and Rutten provide a criterion for the existence of a solution, namely the contractiveness of the respective functor. Contractiveness together with an additional criterion, the hom-contractiveness was shown by America and Rutten to guarantee uniqueness. The problem of uniqueness is the topic of our contribution.