Related papers: Topological structures of vague soft sets
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We show how topology of a space may lead to tensor fields on (the smooth part of) moduli spaces of the fundamental group.
Topological Structures in the Standard Model at high $T$ are discussed.
In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
In this paper, the definitions of soft {\Gamma}-semirings and soft sub {\Gamma}-semi rings are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the mean time, some of their properties and structural…
We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the…
We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.
Based on the in-depth analysis of the nature and features of vague phenomenon, this paper focuses on establishing the axiomatical foundation of the membership degree theory for vague phenomenon, presents an axiomatic system of governing…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
Ontologies can be a powerful tool for structuring knowledge, and they are currently the subject of extensive research. Updating the contents of an ontology or improving its interoperability with other ontologies is an important but…
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…
Topological acoustics is an emerging field that lies at the intersection of condensed matter physics, mechanical structural design and acoustics engineering. It explores the design and construction of novel artificial structures, such as…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology.
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
In this paper, we give a complete description of the deformation classes of real structures on minimal ruled surfaces. In particular, we show that these classes are determined by the topology of the real structure, which means that real…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…