  In this paper, we introduce the concept of residuated implications derived
from quasi-overlap functions on lattices and prove some related properties. In
addition, we formalized the residuation principle for the case of quasi-overlap
functions on lattices and their respective induced implications, as well as
revealing that the class of quasi-overlap functions that fulfill the
residuation principle is the same class of continuous functions according to
topology of Scott. Also, Scott's continuity and the notion of densely ordered
posets are used to generalize a classification theorem for residuated
quasi-overlap functions. Finally, the concept of automorphisms are extended to
the context of quasi-overlap functions over lattices, taking these lattices
into account as topological spaces, with a view to obtaining quasi-overlap
functions conjugated by the action of automorphisms.
