On (semi)topological residuated lattices

Abstract

In this paper, we define the notions of semitopological and
topological residuated lattices and derive here conditions that
imply a residuated  lattice to be a semitopological or topological
residuated lattice. Also, we study  the relationship between
separation axioms T0, T1, T2 and (semi)topological residuated lattices.