Topological Residuated ‎Lattices

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $\alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $\alpha$. In the follows, we obtain some conditions on (semi) topological residuated lattices under which this spaces will convert into regular and normal spaces. Finally by using of regularity and normality, we convert (semi)topological residuated lattices into metrizable topological residuated ýlattices.ý