The German mathematician Klaus Janich has a wonderful response to this question in his book on topology, which is intentionally very. Topology. Klaus Janich. This is an intellectually stimulating, informal presentation of those parts of point set topology that are of importance to the nonspecialist. Topology by Klaus Janich: Forward. Content. Sample. Back cover. Review.
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Willard’s book is great, but probably too advanced for the students in question. Textbook in Problems, by O. Willard’s General Topology is my favourite book on point-set topology together with Bourbaki, but the latter is not suited as course text for several topologj. In fact, people communicating in this “paper currency” is kklaus of the primary reasons I have an account on this site; to resolve the questions that arise from imprecise talk. SeebachPaperback, Reprint. Or, closer to topology, I could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere.
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Harry Potter Years by J. It’s a great book to introduce applied topology, although it stops just short of using groups.
It covers topics such as completeness and compactness extremely well. About this product Synopsis Contents: No one quite seems to have figured out yet how to effectively interpolate between the 2 approaches in topolohy textbook.
Of course every mathematician should verify a claim until he feels comfortable that if necessary, he could produce the real argument down to the atomic details. I took the course from Willard and found it fine.
You just have to remember what the topology is defined as for quotient spaces, etc. Janich, Topology jlaus 49,translation by Silvio Levy It was later said by Levy that Janich told him that this particular passage was inspired by Janich’s concerns that German mathematical academia and textbooks in particular were beginning to become far too axiomatic and anti-visual and that this was hurting the clarity of presentations to students.
Any Condition Any Condition. In particular, the motivation of compactness is the best I’ve seen. I’m very fond of Munkres – Topology.
Undergraduate Texts in Mathematics: Well said, although the thing I really don’t like about intuitive handwaving is that intuition differs from person to person. I only looked at the first file in each batch, trusting that the translations work the same way. Home Questions Tags Users Unanswered. From several points of view i. Kosniowski, A first course in algebraic topology; L. Can you provide some more details? The exercises are extensive and very helpful.
algebraic topology – How much rigour is necessary? – Mathematics Stack Exchange
Skip to main content. From chapter 5 and on it provides one of the most modern theoretical works in Topology and group theory and their inter-relationships. But I think Janich has given some quite good advice to the novice here.
Anyway, I read Hatcher only a few months ago to study for a qualifying exam.
textbook recommendation – A book in topology – MathOverflow
The German mathematician Klaus Janich has a wonderful response to this question in his book on topoloyg, which is intentionally very non-rigorous and intuitive: One of the main problems I am facing with the textbook is its level of rigour. Additional Details Number of Volumes. How much rigour is necessary?
I actually don’t know. Sign up using Facebook. Although the second part of the book dealing with Algebraic Topology is not as good as other specialized books in AT such as Hatcher’s book which is free to download on Hatcher’s site. Hocking and Gail S.
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (1994, Hardcover)
I never tried printing it. For me, this level of “rigor” required lies somewhere between explicitly writing out everything in bare bones set theoretic terms, and the level of detail presented in a graduate analysis text such as Rudin. It also addresses a lot of matters like uncountable ordinals that students will likely not have seen, but which are useful in understanding the role of paracompactness, for example.
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