Related papers: Which Topologies induced by order convergences
A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have been defined for the two-letter alphabet only, and the…
A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…
We investigate the interplay of generalized global symmetries in 2+1 dimensions in a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of…
We study how forcing algebras give rise to ${\mathbb A}^1$-bundles and ${\mathbb A}^1$-torsors and how they are related to ${\mathbb A}^1$-patches. In particular we discuss the affineness of torsors and how algebraic properties of ${\mathbb…
In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not…
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }
We prove that the topological cycles of an arbitrary infinite graph induce a matroid. This matroid in general is neither finitary nor cofinitary.
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate or limit navigation of problem spaces by aligned parts thus…
We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as the cases of effectively defocusing and…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the two component system, are more stable than…
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…