Abstract In this note we study order reversing quasi involutions and their properties. These maps are dualities (order involutions) on image. We prove that any involution is induced by a cost. Invariant sets of special interest provide several results regarding existence uniqueness. determine when an sub-class can be extended to the whole space discuss uniqueness such extension. also ways for c...

Abstract We present a special issue reviewing various topics that include: classical and quantum integrability, integrable deformations, the 4D Chern–Simons theory, double field theory α ′ ...