相关论文: PCF Theory
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
This is a draft version of Part II of a three-part textbook on quantum field theory.
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.
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 provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
An expository hitchhikers guide to some theorems in mathematics.
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical…
In this short paper we review and extract some features of the Fredholm Alternative problem .
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.