THE RELATIONSHIP BETWEEN L-FUZZY PROXIMITIES AND L-FUZZY QUASI-UNIFORMITIES

In this paper, we investigate the $L$-fuzzy proximities and the relationships between $L$-fuzzy topologies, $L$-fuzzy topogenous order and $L$-fuzzy uniformity. First, we show that the category of $L$-fuzzy topological spaces can be embedded in the category of $L$-fuzzy quasi-proximity spaces as a coreflective full subcategory. Second, we show that the category of $L$-fuzzy proximity spaces is isomorphic to the category of $L$-fuzzy topogenous order spaces. Finally, we obtain that the category of $L$-fuzzy proximity spaces can be embedded in the category of $L$-fuzzy uniform spaces as a bireflective full subcategory.