On the reflection invariance of residuated chains (Q1035657)

Residuated chains and left-continuous t-norms are investigated in this paper. One of the recent approaches to the study of residuated lattices is the so-called geometric approach. It has shed some light on their algebraic structure and as well to their analytic properties. In this paper it is shown that, under certain conditions, a subset of the graph of a commutative residuated chain is invariant under a geometric reflection. This result implies that a certain part of the graph of the monoidal operation of a commutative residuated chain determines another part of the graph via the reflection and tells us something about the structure of the continuity points of the monoidal operation.