Topological Residuated ‎Lattices

Subject Areas : International Journal of Industrial Mathematics

N.  Kouhestani‎ ¹ (Fuzzy Systems Research Center, University of Sistan and Baluchestan, Zahedan, Iran.)
R. A.  Borzooei‎ ² (Department of Mathematics, Shahid Beheshti University, Tehran, Iran.)

Received: 2017-06-08 Accepted : 2017-06-08 Published : 2017-07-01

Keywords: Topological residuated lattice, ‎F‎ilter, Regular space, Normal space, (locally) Compact ‎space.‎,

Abstract :

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 ‎lattices.‎