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.