)基础拓扑学
- This book includes basic material on general topology, introduces algebraic topology via the fundamental group and covering spaces, and provides a background on topological and smooth manifolds. It is written mainly for students with a limited experience in mathematics, but determined to study the subject actively. The material is presented in a concise form, proofs are omitted. Theorems, however, are formulated in detail, and the reader is expected to treat them as problems.
- 拓扑学是数学中一个重要的、基础性的分支。它最初是几何学的一个分支，主要研究几何形势分析学图形在连续变形下保持不变的性质，现在已成为研究连续性现象的重要的数学分支。
拓扑学起初叫形势分析学，是莱布尼茨1679年提出的名词。十九世纪中期，黎曼在复函数的研究中强调研究函数和积分就必须研究形势分析学。从此开始了现代拓扑学的系统研究。
连续性和离散性是自然界与社会现象中普遍存在的。拓扑学对连续性数学是带有根本意义的，对于离散性数学也起着巨大的推动作用。拓扑学的基本内容已经成为现代数学的常识。拓扑学的概念和方法在物理学、生物学、化学等学科中都有直接、广泛的应用。
