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This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures.
GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory.
For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
|A Note to the Reader|
|Pt. I||General Topology|
|Ch. 1||Set Theory and Logic||3|
|Ch. 2||Topological Spaces and Continuous Functions||75|
|Ch. 3||Connectedness and Compactness||147|
|Ch. 4||Countability and Separation Axioms||189|
|Ch. 5||The Tychonoff Theorem||230|
|Ch. 6||Metrization Theorems and Paracompactness||243|
|Ch. 7||Complete Metric Spaces and Function Spaces||263|
|Ch. 8||Baire Spaces and Dimension Theory||294|
|Pt. II||Algebraic Topology|
|Ch. 9||The Fundamental Group||321|
|Ch. 10||Separation Theorems in the Plane||376|
|Ch. 11||The Seifert-van Kampen Theorem||407|
|Ch. 12||Classification of Surfaces||446|
|Ch. 13||Classification of Covering Spaces||477|
|Ch. 14||Applications to Group Theory||501|
Posted December 16, 2000
This second edition is an overwhelming victory over not only most other textbooks in this realm of mathematics but also over its predecessor first edition. What distinguishes this textbook from others is that there is a clear boundary set forth between the contents in general topology and algebraic topology as well as the lucid exposition of the abstract concepts encountered in topology. With a more thorough coverage of the subject, this second edition brings even more delightful surprises to anyone both ardent and serious about exploring the abstract realm of advanced mathematics!! I definitely keep this book along with the first edition that I had used for my first course in topology!Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.