Test spaces (or manuals) provide a simple, elegant and very general mathematical framework for the study of probability theory – classical, quantum and otherwise. In many particular cases of interest, test spaces carry significant topological structure. This paper inaugurates a general study of topological test spaces. Among other results, we show that any topological test space with a compact ...

Topological charge distributions in 2 dimensional CP 2 model with θ-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this behavior leads to the first order phase transition at θ = π. In weak coupling regions it shows non-Gaussian distribution and the first order phase transition disapp...

Current theories of Kondo insulators employ the interaction of conduction electrons with localized Kramers doublets originating from a tetragonal crystalline environment, yet all Kondo insulators are cubic. Here we develop a theory of cubic topological Kondo insulators involving the interaction of Γ(8) spin quartets with a conduction sea. The spin quartets greatly increase the potential for str...

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories — in particular, the standard cosimplicial topological space can be produced.