相关论文: Notes on topological vector spaces

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…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…

We find universal spaces for Alexandroff and finite spaces and explore some of its topological properties as well as their description as inverse limits of finite spaces and Alexandroff extensions. They can be used as a natural environment…

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.

These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…

In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.

This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.

We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by…

The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…

This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…

Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.

This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.