In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rat...

Set constraints are inclusions between expressions denoting sets of ground terms over a finite ranked alphabet Σ. Rational spaces are topological spaces obtained as spaces of runs of topological Σhypergraphs. They were introduced by Kozen in [Koz95], where the topological structure of the spaces of solutions to systems of set constraints was given in terms of rational spaces. In this paper we c...