Prime elements of non-integral quantales and their applications.
The first three sections of this well-written article provide a very readable introduction to quantales, culminating in the question: Which type of space corresponds to a spatial quantale? Towards answering that question, the author introduces in section 4 the involutive semi-integral quantale \(Q(2)\), and relates it to prime elements. The answer to the question is then explained in section 5, using multi valued topologies, summarized as Fact II: Semiunital spatial quantales and \(Q(2)\)-valued sober spaces are equivalent concepts. The final section gives an application to the topologization of the spectrum of \(C^*\)-algebras.
scientific article; zbMATH DE number 6506232
scientific article