Given a fuzzy finite state machine M = (Q, Σ, μ), a fuzzy closure operator is defined which induces a Lowen-type fuzzytopology τ in Q. The concepts of separation of fuzzy subsystems and connectedness of fuzzy finite state machines aredeveloped. Some results on connectedness and weak connectedness of fuzzy subsystems are obtained. Characterizationsof these concepts in terms of the fuzzy topology are also obtained.