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On L-Fuzzy Topological Spaces Determined by Implicators

    This paper is towards the study of L-fuzzy topological spaces, L-fuzzy pretopological spaces and their corresponding operators determined by general implicators. We show that the results regarding one-to-one correspondence between L-fuzzy reflexive approximation spaces and L-fuzzy pretopological spaces as well as L-fuzzy preorder approximation spaces and L-fuzzy topological spaces heavily depend on implicators. Finally, we establish a relationship between category of L-fuzzy pretopological spaces and category of L-fuzzy topological spaces by using category of L-fuzzy approximation spaces.