In the current study, we define the different L-valued operators on L ᴮ-valued general fuzzy automata or simply L ᴮ-valued GFA, where B is considered as a complete infinitely distributive lattice of propositions about the GFA. In particular, this study demonstrates that the L-valued successor and predecessor operators induce L-valued co-topologies while the L-valued residuated and approximation operators induce L-valued topologies on the state set of given L ᴮ-valued GFA. Further, we show that the continuity and separation properties of such Lᴮ-valued general fuzzy automaton can be examined in terms of these topologies. Moreover, we study and explicate the Lᴮ-valued GFA structure space and Lᴮ-valued GFA homotopy in more details.