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内容简介
This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or "combinatorial," topology. There was earlier scattered work by Euler, Listing (who coined the word "topology"), M/Sbius and his band, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or "analysis situs" as it was often called at the time) as a coherent theory, however, belongs to Poincar6.
Curiously, the beginning of general topology, also called "point set
topology," dates fourteen years later when Fr6chet published the first abstract treatment of the subject in 1906.
Since the beginning of time, or at least the era of A'rchimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have always been at the core of interest in topology. After the seminal work of Milnor, Smale, and many others, in the last half of this century, the topological aspects of smooth manifolds, as distinct from the differential geometric aspects, became a subject in its own right. While the major portion of this book is devoted to algebraic topology, I attempt to give the reader some glimpses into the beautiful and important realm of smooth manifolds along the way, and to instill the tenet that the algebraic tools are primarily intended for the understanding of the geometric world.
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[您可以向编辑推荐本书的亮点，采纳后奖励５－１０元优惠卷]（一个工作日内处理您的建议）
本书是一部比较原始但又不失趣味性的拓扑与几何课本，完全是从现代观点研究问题，可以说是25年以来，继Spanier之后真正的一本全新的拓扑书。很适合作为一年级研究生的代数拓扑教科书。内容安排紧凑、合理，从一般拓扑开始，讲述了微分流形，上同调，乘积和对偶，基础群，同调理论和同伦理论。包括了面理论，群理论，和纤维丛理论这些大多数拓扑学家想让学拓扑的学生了解的知识点。并且有很多内容很具有启发性，这些内容并不是所有传统的课本中都包含的。通过这本书的阅读也可以提高数学学习能力。
尽管这本书具有很强的综合性，但并没有过分去去囊括多余的综合材料，而是这些材料真正地提高了表述的效率和清晰度。
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读者：scubookworm 最新讨论：2008-6-30 21:37:13 评价等级：
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| 如果你想学习拓扑学，那么选择本书就非常明智。虽然阅读本书需要一定的数学"成熟度"，但本书胜在其选材范围和论述的清晰明了。本人唯一感到遗憾的是：应该增加一个专门讲解基础范畴论的附录，如果有的话就完美了。作者Bredon不太常用范畴的语言(虽然是以一种非本质的方式)。因为本书是面向一年级的研究生，故而默认学生已经有了这方面的知识。这就是本人对这本书的一点小小报怨，其它的无可挑剔！强烈推荐！
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