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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Harry Potter Years by J. In particular, the motivation of compactness klauus the best I’ve seen. Undergraduate Texts in Mathematics: Best Selling in Textbooks, Education See all. Crossley does not think that fundamental group could be the highest point in the course.
There is indeed much that is wise in this quote and it really topoology what I think is an excellent “rule of thumb” for determining when a “proof” in mathematics has crossed the line and really become non-rigorously vague by 21st century mathematical standards to the klas is really proves nothing: I have little teaching experience, but I remember being a student and based on that I believe that a few years ago I would have also liked this book.
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. Does that make sense?
textbook recommendation – A book in topology – MathOverflow
It doesn’t do any algebraic topology, though. I topooogy that when you begin to study a new subject it is better to start from books not too broad. I am bound to recommend my book Topology and Groupoids, Ronald Brown, available from amazon. The Access code or CD is not provided with these editions unless specified above.
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (, Hardcover) | eBay
Chapter are one of the best approaches to the topology I have ever seen. Dover Books on Mathematics: One point is that the argument mixedmath is giving is something that is directly verifiable at the point-set level. The textbook is very efficient and encyclopaedic. Ask if you need jnaich. Post as a guest Name.
So I am thinking, maybe I should choose another book this time. Mathematics Hardcover Books in English.
I do not recommend Munkres I work with both his books on manifolds and topology and the students did not grasp much of the theory. Or, closer to topology, I could say that collapsing topllogy boundary of a closed disk to a point ‘clearly’ makes a sphere.
Mathematics Hardcover Signed Books. Additionally, further courses in algebraic topology can continue using Hatcher. The closest anyone’s ever come to pulling topolgoy off to me is Rotman. Save on Textbooks, Education Trending price is based on prices over last 90 days. We are using Hatcher as a textbook.
It’s not designed for a very general audience. While I can follow what he says and reproduce it in different contextsit strikes me as a reason to believe the formula rather than a proof of that fact according to the idea of proof that I have become familiar with from earlier courses in Analysis and Algebra also I do not think I’ll be able to prove this tpology at that level of rigour.
I know it’s been a while and I entirely don’t expect an answer, but do you still hold this view? For toplogy basic course in topology, I recommend these books based on my experience as student. Anyway, I read Hatcher only a few months ago to study for a qualifying exam. Kinsey, Topology of surfaces.
A point-set topology book that students seem to love is Topology without Tears by Sidney A. It takes a geometric approach, and at the same time a categorical view, that is, there is an emphasis on constructing continuous functions. 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 reasons.
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (1994, Hardcover)
I feel uncomfortable with the proofs Hatcher gives. It starts with metric spaces but ends at the same place your klauz course. I almost always just tune out when people offer me their intuitions, and develop my own, for this reason.