Abstract

this paper will be realizations. The category of Boolean operations and their property-preserving renamings is not self-dual since non-T 0 Chu spaces transpose to nonextensional ones. By the same reasoning the full subcategory consisting of T 0 operations, those with no properties a j b for distinct variables a; b, is self-dual. This is a very important fact: it means that to every full subcategory C of this self-dual category we may associate its dual as the image of C under the self-duality. This associates sets to complete atomic Boolean algebras, Boolean algebras to Stone spaces, distributive lattices to Stone-Priestley posets, semilattices to algebraic lattices, complete semilattices to themselves, and so on for many other familiar [Joh82] and not so familiar (self-duality of finite-dimensional vector spaces over GF (2)) instances of Stone duality We now illustrate the general idea with some examples.

Citations