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Under a general categorical procedure for the extension of dual equivalences as presented in this papers predecessor, a new algebraically defined category is established that is dually equivalent to the category $bf LKHaus$ of locally compact Hausdorff spaces and continuous maps, with the dual equivalence extending a Stone-type duality for the category of extremally disconnected locally compact Hausdorff spaces and continuous maps. The new category is then shown to be isomorphic to the category $bf CLCA$ of complete local contact algebras and suitable morphisms. Thereby, a new proof is presented for the equivalence ${bf LKHaus}simeq{bf CLCA}^{rm op}$ that was obtained by the first author more than a decade ago. Unlike the morphisms of $bf CLCA$, the morphisms of the new category and their composition law are very natural and easy to handle.
Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category $bf KHaus$ of compact Hausdorff spaces and their continuous maps, as an extension of a restricted Ston
This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finettis representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad.
Internal preneighbourhood spaces were first conceived inside any finitely complete category with finite coproducts and proper factorisation structure in my earlier paper. In this paper a closure operation is introduced on internal preneighbourhood sp
Profinite algebras are the residually finite compact algebras, whose underlying topological spaces are Stone spaces. We introduce Stone pseudovarieties, that is, classes of Stone topological algebras of a fixed signature that are closed under taking
Given a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X we extend the semigroup operation of X to a right-topological semigroup operation on TX whose topological center contains the dense subs