In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology (so called (2, L)-fuzzy topology) as L-concepts where L is a complete residuated lattice. The concepts of (2, L)-derived, (2, L)-closure, (2, L)-interior, (2, L)-exterior and (2, L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2, L)-topology. As applications of our work the corresponding results (see [10?11]) are generalized and new consequences are obtained.

Keywords: L-fuzziying topology,convergence of nets,convergence of filters,bases,subbases and Complete residuated lattice