AbstractIn this paper, we are studying about a function’s between domain ζ-nano topological spaces and codomain nano topological spaces which means every nano topology has its inverse image in ζ-nano topology(i.e., ζ-continuous). We establish the ζcluster point in ζ-continuous. We search image from a ζ-open sets (ζ-closed set) to a nano open sets(nano closed sets) is called a ζ-open map(ζ-closed map). Finally, some of the results are portrayed with these ζ-continuity with N -continuity and we extended to ζ-homeomorphism.