相关论文: Notes on topological vector spaces
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
Gradient vector fields are fundamental objects from both theoretical and practical perspectives, since various phenomena can be modeled within this framework. The ``moduli space'' of such vector fields provides the foundation for describing…
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…
The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…
In this paper, we analyze the definition Andr\'e proposed for near-vector spaces to make it more transparent. We also study the class of near-vector spaces over division rings and give a characterization of regularity that gives a new…
The notion of sobriety is extended to the realm of topological spaces valued in a commutative and unital quantale, via an adjunction between a category of quantale modules and the category of quantale-valued topological spaces. Relations…
This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.
We study some topological properties of attractors.
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
We construct in ZFC an L topological vector space -- a topological vector space that is an L space -- and an L field -- a topological field that is an L space. This generalizes results in [5] and [8].
These informal notes are concerned with sums and averages in various situations in analysis.
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.