Sobriety and spatiality in varieties of algebras (Q835242)

This paper extends the fundamental adjunction between the categories of topological spaces and locales (that paved the ground for the development of locale theory and point-free topology), and its analogue for fuzzy topology, to an arbitrary variety of algebras \textbf{A}. For this, the author introduces the category \(Q\)-\textbf{Top} of \(Q\)-topological spaces and \(Q\)-continuous maps, for an algebra \(Q\) of \textbf{A}. The corresponding notions of \(Q\)-sobriety and \(Q\)-spatiality are studied in detail and the obtained results are illustrated in the category of algebras over a given unital commutative quantale.