L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

In the present paper we introduce and study L-pre-T0-, L-pre-T1-, L-pre-T2 (L-pre-Hausdorff)-, L-pre-T3 (L-preregularity)-, L-pre-T4 (L-pre-normality)-, L-pre-strong-T3-, L-pre-strong-T4-, L-pre-R0-, L-pre-R1-separation axioms in (2, L)-topologies where L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the ”∧” is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results (see [1, 2]) are generalized and new consequences are obtained.