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- $T_0$ -, L-pre- $T_1$ -, L-pre- $T_2$ (L-pre-Hausdorff)-, L-pre- $T_3$ (L-pre-regularity)-, L-pre- $T_4$ (L-pre-normality)-, L-pre-strong- $T_3$ -, L-pre-strong- $T_4$ -, L-pre- $R_0$ -, L-pre- $R_1$ -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 " $\bigwedge$ " 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.
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