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Algebraic Topology (Dover Books on Mathematics)

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undefinedBased on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern of elementary algebraic topology, essentially from a topy theoretic viewpoint. The presentation of the topy theory and the account of duality in logy manifolds make the text ideal for a course on either topy or logy theory. The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the logy or topy groups of a topological space. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds. Other important topics covered are topy theory, CW-complexes and the co-logy groups associated with a general Ω-spectrum. Dr. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results. "Throughout the text the style of writing is first class. The author has given much attention to detail, yet ensures that the reader knows where he is going. An excellent book." — Bulletin of the Institute of Mathematics and Its Applications.

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