This paper applies a combination of algebraic and topological methods to obtain new and structural results on mp- and purified residuated lattices. It is demonstrated that mp-residuated lattices are strongly tied up with the dual hull-kernel topology. Mainly, it is shown that a residuated lattice is mp if and only if its minimal prime spectrum, equipped with the dual hull-kernel topology, is Hausdorff if and only if its prime spectrum, fitted with the dual hull-kernel topology, is normal. For a residuated lattice and a subalgebra , the notion of disjunctive -regular and -mp-residuated lattices are introduced and investigated. It is shown that a residuated lattice is purified if and only if it is -mp if and only if it is disjunctive -regular, where is the set of complemented elements of . Some topological characterizations for purified residuated lattices are extracted and proved that a residuated lattice is purified if and only if its minimal prime spectrum, equipped with the dual hull-kernel topology, is a profinite space. To support mentioned concepts, we give place to some examples.