Related papers: A representation of sup-completion

A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving subset that can be written as an at most countably infinite…

We study the Cox realization of an affine variety, i.e., a canonical representation of a normal affine variety with finitely generated divisor class group as a quotient of a factorially graded affine variety by an action of the Neron-Severi…

It is known from Grzegorczyk's paper \cite{grze-1951} that the lattice of real semi-algebraic closed subsets of ${\mathbb R}^n$ is undecidable for every integer $n\geq 2$. More generally, if $X$ is any definable set over a real or…

Let $C$ be a cone in a locally convex Hausdorff topological vector space $X$ containing $0$. We show that there exists a (essentially unique) nonempty family $\mathscr{K}$ of nonempty subsets of the topological dual $X^\prime$ such that $$…

Working in the setting of $\infty$-categories, we develop a general theory of the codensity monad $T_\mathcal{D}$ associated with a full subcategory $\mathcal{D}\subseteq \mathcal{C}$. We show that $T_\mathcal{D}$ has a canonical monad…

We introduce a class of decorated abstract graphs, that we call XC-tangles, that provides a very convenient framework to study quantum invariants of tangles and virtual tangles. These can be viewed as a far-reaching generalisation of…

We give a pedagogical presentation of the irreducible unitary representations of $\mathbb{C}^4\rtimes\mathbf{Spin}(4,\mathbb{C})$, that is, of the universal cover of the complexified Poincar\'e group…

For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identified with the Stone space $\px$. Via this…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

The existing analyses on the X(3872) lineshape are consistent with the hypothesis that it is a compact particle composed of four quarks. This conclusion follows from fitting available data with a Flatte' distribution derived from an…

Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…

We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…

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…

The functionals on an ordered semigroup S in the category Cu--a category to which the Cuntz semigroup of a C*-algebra naturally belongs--are investigated. After appending a new axiom to the category Cu, it is shown that the "realification"…

The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the…

In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spanned vector space) into which it embeds as a generating…

We establish a Crapo complementation formula for the M\"obius function $\mu^X$ in a general decomposition space $X$ in terms of a convex subspace $K$ and its complement: $\mu^X \simeq \mu^{X\setminus K} + \mu^X*\zeta^K*\mu^X$. We work at…

For a coisotropic (or first-class) submanifold C of a Poisson manifold X we consider star-products for which the vanishing ideal I of C becomes a left ideal in the deformed algebra thus defining a left module structure on the space of…

In Sternfeld's work on Kolmogorov's Superposition Theorem appeared the combinatorial-geometric notion of a basic set and a certain kind of arrays. A subset $X \subset \mathbb R^n$ is basic if any continuous function $X\to \mathbb R$ could…