On the Uniqueness of Fixed Points of Endofunctors in a Category of Complete Metric Spaces

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.