A topological approach to MTL-algebras

We give a dualized construction of Aguzzoli–Flaminio–Ugolini of a large class of MTL-algebras from quadruples (B, A, v, d), consisting of a Boolean algebra B, a generalized MTL-algebra A, and maps v and d parameterizing the connection between these two constituent pieces. Our dualized construction gives a uniform way of building the extended Priestley spaces of MTL-algebras in this class from the Stone spaces of their Boolean skeletons, the extended Priestley spaces of their radicals, and a family of maps connecting the two. In order to make this dualized construction possible, we also present novel results regarding the extended Priestley duals of MTL-algebras and GMTL-algebras, in particular emphasizing their structure as Priestley spaces enriched by a partial binary operation.