Related papers: Closed injective systems and its fundamental limit…
Black holes are extraordinary massive objects which can be described classically by general relativity, and topological insulators are new orders of matter that could be use to built a topological quantum computer. They seem to be different…
This paper introduces a novel class of topological spaces, termed SC*-regular spaces, which are defined using SC*-open sets. We explore their fundamental properties and examine their connections with existing regularity concepts, such as…
We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…
In this paper we address two questions concerning the effective action of a topological insulator in one and three dimensional space without boundaries, such as a torus. The first is whether a uniform $\theta$-term with $\theta=\pi$ is…
In these notes the epitopological and pseudotopological fundamental group functors are introduced. These are functors from the category of pointed epitopological and pseudotopological spaces respectively, to the category of their respective…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
The main aim of this paper is to provide a description of neighbourhood operators in finitely complete categories with finite coproducts and a proper factorisation system such that the semilattice of admissible subobjects make a…
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then…
A saturated fusion system over a finite $p$-group $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over $S$ is realized…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
In this paper we generalize a shift theorem, which plays a key role in studying representations of FI$^m$, the product category of the category of finite sets and injections, and classify finitely generated injective FI$^m$-modules over a…
Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with a family of 'directed paths', closed under some operations.…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…