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 in topology Ask Question. Can you provide some more details?
Undergraduate Texts in Mathematics: Topology by Klaus Jänich (, Hardcover) | eBay
The down side of this approach is that it completely disconnects the subject from it’s geometric roots and it becomes simply another branch of algebra whose roots are utterly mysterious.
The students learn the concepts fast, their theoretical language to explicate honed, and their visualization skills improved.
See details for additional description. I will have to teach a topology course: No one quite seems to have figured out yet how to effectively interpolate between the 2 approaches in a textbook. You just have to remember what the topology is defined as for quotient spaces, etc.
Immediately after proving that there is no retraction from the disk onto its circle boundary, they use degree theory to analyze sudden cardiac death. This book is excellent jwnich visualization and at the same precise theoretical treatment of the subject.
In the past I have used two different books: So as jancih of a course in analysis I used as a source R. 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)
What have they seen and not seen yet? Best Selling in Textbooks, Education See all. I actually don’t know.
While this is intuitively clear, it requires some work to prove. Looking back, I was never uncomfortable with the kind of justifications we used to give in high school calculus and this current discomfiture stems from the fact that I have taken a few courses in Analysis in between. A fairly streamlined book, although initially gentle, is Essential Topology by Janih.
I should say that I chose the groupoid view in the first edition as it seemed to me more intuitive and more powerful. Even with an American printer, it looks like I could print it with no more trouble than funny margins. For a basic course in topology, I recommend these books based on my experience as student.
Kosniowski, A first course in algebraic topology; L. In fact, people communicating in this “paper currency” is one of the primary reasons I have an account on this site; to resolve the questions that arise from imprecise talk. I took the course from Willard and found it fine. You get all the advantages of two more specialized textbooks, and topologg Hatcher’s text is free, your students won’t need to buy two textbooks.
The level of rigor that is needed depends on your own taste. It covers topics such as completeness and compactness extremely well.
A wise choise because Kosniowski’s “A first course in algebraic topology” is an user-friendly book to learn basic definitions and theorems about general topology, homotopy theory and fundamental group. Some relevant remarks by Terry Tao. My answer was you should not change your first choise. RowlingHardcover Sign up using Facebook.