A topology based on nuclei and upsets in residuated lattices.

Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices. [ABSTRACT FROM AUTHOR]