Categorical Extension of Dualities: From Stone to de Vries and Beyond, II

Abstract

Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category $\mathbf{LKHaus}$ 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 $\mathbf{CLCA}$ of complete local contact algebras and suitable morphisms. Thereby, a new proof is presented for the equivalence $\mathbf{LKHaus}\simeq {\mathbf{CLCA}}^{\mathrm{op}}$ that was obtained by the first author more than a decade ago. Unlike the morphisms of $\mathbf{CLCA}$, the morphisms of the new category and their composition law are very natural and easy to handle.

32 pages

References in corpus (1)

• A De Vries-type Duality Theorem for Locally Compact Spaces -- II