Related papers: Density in categorical topology via quantaloid-enr…

We study an open question at the interplay between the classical and the dynamical Mordell-Lang conjectures in positive characteristic. Let $K$ be an algebraically closed field of positive characteristic, let $G$ be a finitely generated…

For a quantale ${\sf{V}}$, the category $\sf V$-${\bf Top}$ of ${\sf{V}}$-valued topological spaces may be introduced as a full subcategory of those ${\sf{V}}$-valued closure spaces whose closure operation preserves finite joins. In…

In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no…

Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational…

We prove that there exists a scrambled set for the Gauss map with full Hausdorff dimension. Meanwhile, we also investigate the topological properties of the sets of points with dense or non-dense orbits.

Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of…

We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite…

The classification of topological materials is revisited using advanced computational workflows that integrate hybrid density functional theory calculations with exact Hartree-Fock exchange. Unlike previous studies, our workflow optimizes…

We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…

We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois…

Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal…

We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a…

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…

We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely…

Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…

The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.

We construct classifying $\infty$-topoi by showing that the $(\infty,2)$-category of topoi has weighted limits. We show that several prestacks of interest have a classifying topos, including the prestack of spectra.

In this article, we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients and their sum. For a finite $p$-group $G$ of rank $n$, we show that the Gaussian binomial coefficient…

Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…