This book is an introduction to manifolds at the beginning graduate level:It contains the essential topological ideas that are needed for the furtherstudy of manifolds, particularly in the context of differential geometry,algebraic topology, and related fields￡?Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of...
This book is an introduction to manifolds at the beginning graduate level:It contains the essential topological ideas that are needed for the furtherstudy of manifolds, particularly in the context of differential geometry,algebraic topology, and related fields￡?Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Here at the University of Washington, for example, this text is used for the first third of a year-long course on the geometry and topology of anifolds; the remaining two-thirds focuses on smooth manifolds.
此书为英文版！
原文摘录
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The usual way to prove that two manifolds are not topologically equivalent is by finding topological invariants:properties(which could be numbers or other mathematical objects such as groups,matrices,polynomials,or vector space)that are preserved by homeomorphisms.If two manifolds have different invariants ,they can not be homeomorphic. (查看原文)
4 有用 邻家大爷 2011-04-04 17:33:21
202 内容很丰富，可作为大二一年一般拓扑与代数拓扑的入门书
0 有用 鱼尾巴 2012-07-30 04:20:52
第二版比较好。。第一版有点乱。。
0 有用 豆友HJh0na3AAI 2024-02-28 21:18:16 广东
读过的唯一一本点集拓扑书。感觉很多微妙之处其实对流形都不起作用啊(≖_≖ )