图书介绍
Beginning topologyPDF|Epub|txt|kindle电子书版本网盘下载
- Sue E. Goodman 著
- 出版社： American Mathematical Society
- ISBN：0821847961
- 出版时间：2009
- 标注页数：236页
- 文件大小：26MB
- 文件页数：253页
- 主题词：
PDF下载
下载说明
Beginning topologyPDF格式电子书版下载
下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！
（文件页数 要大于 标注页数，上中下等多册电子书除外）
注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具
图书目录
1INTRODUCTION TO POINT SET TOPOLOGY1
1.1 Open and Closed Sets1
1.2 Continuous Functions12
1.3 Some Topological Properties22
1.4 A Brief Introduction to Dimension（Optional）31
2SURFACES36
2.1 Definition of a Surface36
2.2 Connected Sum Construction39
2.3 Plane Models of Surfaces41
2.4 Orientability54
2.5 Plane Models of Nonorientable Surfaces56
2.6 Classification of Surfaces57
2.7 Proof of the Classification Theorem for Surfaces（Optional）59
3THE EULER CHARACTERISTIC66
3.1 Cell Complexes and the Euler Characteristic67
3.2 Triangulations75
3.3 Genus77
3.4 Regular Complexes80
3.5 b-Valent Complexes86
4MAPS AND GRAPHS90
4.1 Maps and Map Coloring91
4.2 The Five-Color Theorem for S298
4.3 Introduction to Graphs101
4.4 Graphs in Surfaces107
4.5 Embedding the Complete Graphs and Graph Coloring113
5VECTOR FIELDS ON SURFACES118
5.1 Vector Fields in the Plane119
5.2 Index of a Critical Point122
5.3 Limit Sets in the Plane131
5.4 A Local Description of a Critical Point133
5.5 Vector Fields on Surfaces141
6THE FUNDAMENTAL GROUP152
6.1 Path Homotopy and the Fundamental Group153
6.2 The Fundamental Group of the Circle160
6.3 Deformation Retracts164
6.4 Further Calculations167
6.5 Presentations of Groups171
6.6 Seifert-van Kampen Theorem and the Fundamental Groups of Surfaces173
6.7 Proof of the Seifert-van Kampen Theorem179
7INTRODUCTION TO KNOTS182
7.1 Knots：What They Are and How to Draw Them183
7.2 Prime Knots190
7.3 Alternating Knots191
7.4 Reidemeister Moves193
7.5 Some Simple Knot Invariants194
7.6 Surfaces with Boundary202
7.7 Knots and Surfaces207
7.8 Knot Polynomials219
Bibliography and Reading List230
Index234