Semantic domains based on sets with families of equivalences

AbstractThis paper contains a preliminary study of a class of spaces that can be seen as special cases of metric spaces. These spaces seem to cover all practical needs, as exemplified e.g. by the work in [2]. Their interest lies mainly in the fact that the degree of mathematical sofistication required to develop the theory is quite small, at least as compared to the metric case. The paper recreates part of the theory developed for metric spaces, ending with a fixed-point theorem that can be used for solving “domain equations”, and a final coalgebra theorem