Related papers: Star-regularity and regular completions
We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here…
This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…
The purpose of this study is to introduce a new class of regular spaces called e*$\theta$-regular spaces which is a generalization of the class of $\beta\theta$-regular spaces. Also, we investigate some basic properties and several…
If $K$ is a field with involution and $E$ an arbitrary graph, the involution from $K$ naturally induces an involution of the Leavitt path algebra $L_K(E).$ We show that the involution on $L_K(E)$ is proper if the involution on $K$ is…
Let $k$ be \emph{any} algebraically closed field in any characteristic, let $R$ be any regular local ring such that $R$ contains $k$ as a subring, the residue field of $R$ is isomorphic to $k$ as $k$-algebras and $\dim R\geq 1$, let $P$ be…
This report is an improvement of a prior report (Report 814). It sharpens the principal theorem (Theorem 5.1 of Report 814) and also simplifies its proof. There are also several minor changes involving clarifications and corrections of…
We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.
We continue studying the properties of $\gamma_0$-compact, $\gamma^*$-regular and $\gamma$-normal spaces defined in [5]. We also define and discuss $\gamma$-locally compact spaces.
The original Lawvere condition asserts that every reflexive graph admits a unique natural structure of internal groupoid. This property was identified by P. T. Johnstone, following a question by A. Carboni and a suggestion by F. W. Lawvere,…
In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank.
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results from [L. Lov\'asz, B.…
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely…
For a star-shaped graph, we introduce special characters and study their properties. We decompose special characters into odd and even parts and study their evolution under reflections. We apply the obtained formulas to prove that the…
The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…
We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This…
We introduce the notion of star-symmetry for relations in a multi-pointed category and use it to obtain a characterization of the projective covers of 2-star-permutable categories. This generalizes the results of Rosick\'y-Vitale for…
Given a graph $H$ on vertex set $\{1,2,\cdots, n\}$ and a function $f:[0,1]^2 \rightarrow \mathbb{R}$, define \begin{align*} \|f\|_{H}:=\left\vert\int \prod_{ij\in E(H)}f(x_i,x_j)d\mu^{|V(H)|}\right\vert^{1/|E(H)|}, \end{align*} where $\mu$…
We take a fresh look at the relationship between $K$-regularity and regularity of schemes, proving two results in this direction. First, we show that $K_2$-regular affine algebras over fields of characteristic zero are normal. Second, we…
The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…
We obtain a rigidity phenomena of rational cohomology automorphisms of certain homogeneous spaces, in the presence of external cohomology classes arising from spaces with trivial cup product in rational cohomology algebra. We classify…