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Foundations of Topology, 2nd  무료배송

 
지은이 : Patty
출판사 : Jones & Bartlett
판수 : 2 edition
페이지수 : 352
ISBN : 9780763742348
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 46,000원 ( 무료배송 )
적립금 : 1,380 Point
   

 



Topology is a branch of pure mathematics that deals with the abstract relationships found in geometry and analysis. Written with the mature student in mind, Foundations of Topology, Second Edition, provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics. The author introduces topics that are well-motivated with thorough proofs, that make them easy to follow. Historical comments are dispersed throughout the text, and exercises, varying in degree of difficulty, are found at the end of each chapter. Foundations of Topology is an excellent text for teaching students how to develop the skills for writing clear and precise proofs.
1. Topological Spaces
2. New Spaces from Old Ones
3. Connectedness
4. Compactness
5. The Separation and Countability Axiom
6. Special Topics
7. Metrizability and Paracompactness
8. The Fundamental Group and Covering Spaces
9. Applications of Homotopy
Appendix A: Logic and Proofs
Appendix B: Sets
Appendix C: Functions
Appendix D: Indexing Sets and Cartesian Products
Appendix E. Equivalence Relations and Order Relations
Appendix F. Countable Sets
Appendix G. Uncountable Sets
Appendix H. Ordinal and Cardinal Numbers
Appendix I. Algebra
"Each section of this text is plagued with typographical errors, many of which alter the meaning of important statements. Long equations are frequently typeset in-line, making much of the text difficult to read. Also, the author should note the words homomorphism and homeomorphism are not interchangeable. The list goes on...

I would not recommend this text for an introductory course, as students will spend more time deciphering the author's intent than learning mathematics."


"We're using this book in my undergrad point-set topology course right now. The definitions and examples are extremely helpful, and overall I love it. There is enough information in the text so that I don't feel it's necessary to buy the Munkres book to supplement my learning, but I did anyway. The appendices in the back are especially amazing since I have not taken an analysis course and because my set theory was a little rusty. I love the appendices.

The main problem is that there are quite a few errors. Generally speaking while reading through a text we can kind of pick out typos just from using our prior knowledge and context clues, but as I had no previous experience in topology or analysis, having to guess whether or not what I was reading was correct significantly slows me down. I was able to find an errata online (just google Patty Topology Errata), which was very helpful.

Overall, it's very functional. The definitions are easy to utilize, there are plenty of robust examples, and there are lots of exercises conducive to working with the material in order to obtain a better understanding of what's going on in topology-land."
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