Topological version of generalized (infinite) iterated function systems

Our paper is an attempt to unify various generalizations of IFSs which appeared in the literature in the last years. We extend the notion of a generalized iterated function system (introduced by Miculescu and Mihail in 2008) to the topological and (possible) infinite case. Then we prove that many classical results (for example the existence of a unique attractor) hold for this extended case.