Lecture Notes on Basic Topology

Author: You Chengye (Editor)
Publisher:
Publish Date: 2004-03-01
Features: This book is an introductory textbook on topology. It covers both point-set topology and algebraic topology, with a focus on the fundamental concepts, methods, and applications of algebraic topology. The book is divided into eight chapters: Basic Concepts of Topological Spaces, Compactness and Connectedness, Quotient Spaces and Closed Surfaces, Homotopy and Fundamental Groups, CW Complexes, Simplicial Homology and Its Applications, Mapping Degree and Fixed Points, etc. Each section is accompanied by a sufficient number of exercises, and solutions and hints are provided at the end of the book. The book is written in an accessible manner with rich examples, rigorous proofs, and clear emphasis on key points. It highlights geometric intuition and aims to cultivate students' geometric thinking skills. The methods presented are innovative, particularly in the calculation of the mapping degree of antipodal mappings. The book closely integrates abstract theory with practical applications, providing students with training in abstract thinking and logical reasoning. This book can serve as a textbook for topology courses in mathematics departments of comprehensive universities and normal universities, and can also be used as a supplementary reading material for relevant science and technology professionals and topology enthusiasts.