This paper is dedicated to introduce the concept of a new space named "L-fuzzy nearness" and to arise a great deal of relationships among it and most of known spaces, like: L-fuzzy topological spaces (interior, closure, co-topology) and L-fuzzy pre-proximities in complete residuated lattices. We have demonstrated concrete functors between the category of Alexandrov L-fuzzy nearness, Alexandrov L-fuzzy topological structures and Alexandrov L-fuzzy pre-proximities and established the Galois correspondence between these categories.
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