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We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
On objects of a triangulated category with a stability condition, we construct a topology.
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
The classical K\"{u}nneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove K\"{u}nneth-type theorems for the persistent homology of the categorical and tensor…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an important construction in graphical models and a standard way…
Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…
We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
We study K-stability of products of K-stable $\mathbb{Q}$-Fano varieties.
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We…
We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
We establish the preservation of the way-below relation with respect to the tensor product.
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
In this article, we study group theoretical embedding properties of subgroups in central products of finite groups. Specifically, we give characterizations of normal, subnormal, and abnormal subgroups of a central product of two groups.
The transfer property for the generalized Browder's theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$-Weyl spectrum inclusion. In addition, the isolated points of…
We describe all adjacency preserving bijections of certain products of Grassmann spaces.
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…