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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A book that I find very readable is “Topology” by John Janicy. Additional Details Number of Volumes. Illustrated Mathematics Hardcover Books. Counter-examples in Topology Author??
algebraic topology – How much rigour is necessary? – Mathematics Stack Exchange
I’d recommend a combination of Munkres and Intuitive topology by V. Nevertheless, this is the best answer I fopology got so far. Crossley does not think that fundamental group could be the highest point in the course. For example, to describe journeys between towns, you look at all journeys, without a special emphasis on return journeys.
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.
Jeff 3, 1 12 Even with an American printer, it looks like I could print it with no more trouble than funny margins. 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. I am taking a course in Algebraic Topology. Thank you very much. Essential Topology looks good, but not suitable for me. Some relevant remarks by Terry Tao.
It also doesn’t have enough theorems and proofs to immerse oneself in the tpoology concepts. If the intuitive argument cannot be rewritten in a completely axiomatic and pedantic manner where there is a completely logical progression from premises to a conclusion, then we should seriously reconsider whether or not jnaich intuitive argument is a valuable one. I only looked at the first file in each batch, trusting that the translations work the same way.
But I think Llaus has given some quite good advice to the novice here. Or a simple closed curve in a plane ‘clearly’ partitions it into two disjoint parts. RowlingHardcover Giving that topology is very terminology-intensive, this is a real problem. But for students that have had a strong set theory or analysis course s beforehand, it’s a great book.
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (, Hardcover) | eBay
I like both of these books and my students hate both of them. Anyway, I read Hatcher only a few months ago to study for a qualifying exam.
What have they seen and not seen yet? In the past I have used two different books: I took the course from Willard and found it fine. It’s not designed for a very general audience.
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (1994, Hardcover)
It also defines the fundamental group, but doesn’t really do anything with it. Sign up or log in Sign up using Google. Best Selling in Textbooks, Education See all. From chapter 5 and on it provides one of the most modern theoretical works in Topology and group theory and their inter-relationships.
Any Condition Any Condition. The exercises are superbly chosen and the examples are wonderful in pushing the theory forwards. It seems to cover a large range of topics, which is nice. Shall we then abandon all intuitive arguments? The German mathematician Klaus Janich has a wonderful response to this question in his book on topology, which is intentionally very non-rigorous and intuitive: Reviews have said that their book is somewhat outdated, but I can’t be sure if that’s the case.