on semitopological de morgan residuated lattices

The class of de morgan residuated lattices was introduced by l. c. holdon (kybernetika 54(3):443-475, 2018), recently, many mathematicians have studied the theory of ideals or filters in de morgan residuated lattices and some of them investigated the properties of de morgan residuated lattices endowed with a topology. in this paper, we introduce the notion of semitopological de morgan residuated lattice, we present some examples and by considering the notion of upsets, for any element a of a de morgan residuated lattice l, there is a topology τa on l and we show that l endowed with the topology τa is semitopological with respect to ∨, ∧ and ⊙, and right topological with respect to → . moreover, in the general case of residuated lattices we prove that l endowed with the topology τa is semitopological with respect to ⊙ and right topological with respect to → . finally, we obtain some of the topological aspects of this structure such as l endowed with the topology τa is a t0-space, but it is not a t1-space or hausdorff space.