Equivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, which called L-enclosed L-internal relations. It is shown that resulting categories isomorphic spaces spaces, respectively.