Related papers: Locally small spaces with an application

Planning methods struggle with computational intractability in solving task-level problems in large-scale environments. This work explores leveraging the commonsense knowledge encoded in LLMs to empower planning techniques to deal with…

We survey different topologizations of the set $\mathcal{S}(G)$ of all closed subgroups of a topological group $G$ and demonstrate some applications in Topological Grous, Model Theory, Geometric Group Theory, Topological Dynamics.

The paper is devoted to generalizations of actions of topological groups on manifolds. Instead of a topological group, we consider a local topological group generalizing the notion of a~germ or a~neighborhood in a topological group. The…

Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between…

Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

We introduce a novel parsing concept called local lexing. It integrates the classically separated stages of lexing and parsing by allowing lexing to be dependent upon the parsing progress and by providing a simple mechanism for constraining…

We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.

Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…

We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a…

We show that cosmological observables can constrain the topology of the compact additional dimensions predicted by string theory. To do this, we develop a general strategy for relating cosmological observables to the microscopic parameters…

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of…

We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…

We have recently begun a project to develop a more effective and efficient way to marshal inferences from background knowledge to facilitate deep natural language understanding. The meaning of a word is taken to be the entities,…