Related papers: Infinitary Noetherian Constructions I. Infinite Wo…
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…
Constructions are given of Noetherian maximal orders that are finitely presented algebras over a field K, defined by monomial relations. In order to do this, it is shown that the underlying homogeneous information determines the algebraic…
Nonstandard analysis is very complex, so finding a simple description of infinitesimal points will be useful. In this paper, ultrafilters as infinitesimal points in a topological space will be proposed, and some topological concepts is…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.
We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
We investigate $\mathcal F$-Borel topological spaces. We focus on finding out how a~complexity of a~space depends on where the~space is embedded. Of a~particular interest is the~problem of determining whether a~complexity of given space $X$…
An algebraic extended bilinear Hilbert semispace is proposed as being the natural representation space for the algebras of von Neumann.This bilinear Hilbert semispace has a well defined structure given by the representation space of an…
We study supertranslations at spatial and future timelike infinity in the first-order formalism. We relax the Ashtekar-Engle-Sloan boundary conditions to allow supertranslations at the spatial infinity and obtain the precise form of the…
We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…
We define $\Delta$-Baire spaces. If a paratopological group $G$ is $\Delta$-Baire space, then $G$ is a topological group. Locally pseudocompact spaces, Baire $p$-spaces, Baire $\Sigma$-spaces, products of \v{C}ech-complete spaces are…
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive…
We consider a product of three copies of infinite symmetric group and its representations spherical with respect to the diagonal subgroup. We show that such representations generate functors from a certain category of simplicial…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…
We construct an infinite family of mutually non-diffeomorphic irreducible smooth structures on the topological 4-manifold $S^2 \times S^2$.
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…