代数拓扑

事实上，熟悉代数拓扑基本原理的读者容易证明这个表示的正确性。

Indeed , readers familiar with the fundamentals of algebriaic topology can easily prove the correctness of this presentation .

文章没有利用代数拓扑知识，而是利用点集拓扑知识证明了Brouwer不动点定理。

Brouwer 's fixed point theorem is shown to make use Of the knowledge of Point set Topology but not to make use of the knowledge of Algebraic Topology .

Eilenberg-MacLane空间是代数拓扑中阻碍理论的核心，是同伦论的重要构成部分。

Eilenberg-MacLane space plays an essential role in Obstruction theory in Algebraic topology . And it is an important part of Homotopy theory .

廖山涛教授的代数拓扑研究工作

The Research Works of Professor S.D. Liao in Algebraic Topology

代数拓扑；辛几何与拓扑；常微分和偏微分方程。

Algebraic Topology ; Symplectic Geometry and Topology ; Ordinary and Partial Differential Equations .

从此，越来越多的代数拓扑学家对这一领域产生了兴趣。

From then on , more and more algebraic topologist become interested in this area .

建议事先知道一些关于代数拓扑和微分几何的基本知识，但不是必需的。

Knowledge of elementary algebraic topology and elementary differential geometry is recommended , but not required .

代数拓扑的一个应用

An application of algebraic topology

你们都对微积分有基本认识并至少学过一年代数拓扑吧

You have a basic understanding of differential calculus and at least one year of algebraic topology ?

习惯上拓扑学被分成点集拓扑、代数拓扑和微分拓扑三部分。

Topology is traditionally decomposed into three parts : General topology , Algebraic topology and Differential topology .

求线图树集的综合方法&二模域代数拓扑树组法

Finding the Tree-Set of Linear Graph by the Method of Topological Tree-Group of the Field Mod 2 Algebra

提出一个基于代数拓扑理论的裂隙网络中流体分布的离散模型。

A fracture network model based on algebraic topology theory has been developed to study fluid flow in the fracture dominant media .

受到代数拓扑的启发，我们发明了一个算法，可以高效单调的减少图嵌入曲面的亏格，并可寻找到称为拟平面图的拓扑曲面。

Inspired by the methods in algebraic topology , we invented an algorithm , which can efficiently reduce the genus , and we can find a quasi-planar graph embedding .

提出了一个非流形结构的表示方法&粘合边结构，其数学基础是代数拓扑中的复形理论。

An identification edge structure is put forward to represent non manifold modeling , which is built on the concepts and methods of the complex and CW complex in algebraic topology .

通过代数拓扑的方法，给出了图的自同态摹群的整矩阵表示，并讨论了整矩阵半群的简单性质。

The integral matrix representation of the endomorphism monoid of a graph has been given by the method of the algebraic topology , some simple properties of the integral matrix semigroup have been discussed .

在另一方面，等变代数拓扑关注于带有群作用的拓扑空间代数不变量的研究，其更深刻的本质在于对空间对称性的揭示，因此从来都在数学研究中占有重要的地位。

On the other hand , equivariant algebraic topology concerns the study of algebraic invariants of space with group actions . It is really a study of symmetries on spaces , and has always occupied a central role in mathematics .

黎曼几何的研究从局部发展到整体，产生了许多深刻的并在其它数学分支，如代数拓扑、偏微分方程、多复变函数论等以及现代物理学中有重要作用的结果。

The investigation of Riemannian geometry , from localization to globe , produced many important results , which can be used in many mathematical fields such as algebra topology , partial differential equation , multiple valued complex analysis as well as modern physics .

具有序结构的Banach空间，容三种最基本的数学结构（代数，拓扑，序）于一体，对它研究无论在理论上还是应用上都有重要的意义。

The Banach space with the ordered structure accommodates three most basic mathematical frameworks ( the algebra , topology , order ) in a body , there is the vital significance in the theory and the application to study for them .

德摩根商拓扑代数的拓扑性质

Properties of Topology in De Morgan Quotient Algebra

拓扑代数的拓扑本原理想

The Topologically Primitive Ideals of Topological Algebras

这一学科的发展受到了数学物理方程和量子力学的推动，它把具体的分析问题抽象到更加纯粹的代数、拓扑结构中进行研究。

The Development of functional analysis has been promoted by equations of mathematical physics and quantum mechanics . It changes specific analytical problems into purer ones of algebra and topology .

MV-代数的Fuzzy拓扑表现定理

The Representation Theorem of MV-algebras by Means of Fuzzy Topology

实直线R上的fuzzy代数与fuzzy拓扑（I）

The Fuzzy Algebra and Fuzzy Topology on Real Line R (ⅰ)

同时讨论了在此定义下子domain的代数性质，拓扑性质及其在解domain方程中的应用。

Meanwhile this paper discuss domain 's algebraic characteristic , topological characteristic and it 's application in solving domain equation .

研究了MV代数的区间拓扑和序拓扑及MV代数下的拓扑紧性、连结性、完备性和全序性。

This paper researched the interval topology and order topology of MV algebra as well as the tightness , connectedness , completeness and the total-orderness of MV algebra .

~EI代数上的拓扑分子格及其在聚类分析中的应用

The Topological Molecular Lattic over ~ EI Algebra and Its Application to Cluster Analysis

关于同调代数与微分拓扑的若干注记

Questions concerning homological algebra and defferential topology

实分片代数曲线的拓扑结构

Topology of piecewise algebraic curves

例如：代数图论、拓扑图论、化学图论、算法图论、随机图论等。

For example , Algebraic graph theory 、 topological graph theory 、 chemical graph theory 、 random graph 、 graph algorithm .

因此可加广义代数格在拓扑中可起与传统代数格在代数中相同的作用。

Thus an additive generalized algebraic lattice will play the same roll in topology as a traditional algebraic lattice has done in algebra .