TUTM. Undergraduate Texts in Mathematics. Klaus Jänich. This is an intellectually stimulating, informal presentation of those parts of point set topology that are. Topology by Klaus Janich: Forward. Content. Sample. Back cover. Review. This is an intellectually stimulating, informal presentation of those parts of point set topology that are of importance to the nonspecialist.
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Learn more about Amazon Giveaway. Counterexamples in Topology;Dover Books on Mathematics. 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.
You just have to remember what the topology is defined as for quotient spaces, etc. Janich, Topology janicy 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.
There is not one part of the book that is not helpful or interesting, and the author delves into many different areas that involve the use of topology. While I agree with the other reviewers here that Jaenich’s “Topology” is very well written, goes to great lengths to explain the “hows and whys” of topology, and includes many, many figures about 1 per page on averageit is probably more popular with people who already know topology than with beginning students, even though it is an introductory text intended for undergraduates.
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 jjanich a few courses in Analysis in between.
Topology : Undergraduate Texts in Mathematics
But I would still consider this as a must-read for all those students who plan on studying mathematics in graduate school. 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 fact at that level of rigour.
Whenever I feel that I am just grinding away at technical results, this is one of the books I return to for a little perspective.
No one quite seems to have figured out yet how to effectively interpolate between the 2 approaches in a textbook. 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.
This text gives the reason behind many advanced topological concepts and tantalizes the reader with it’s varied applications.
While this is intuitively clear, it requires some work to prove. Please try again later. See and discover other items: But, is this the right level of rigour?
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Topology : K Janich :
So allow me topollogy clarify. The level of rigor that is needed depends on your own taste. One of the main problems I am facing with the textbook is its level of rigour. Just by looking at the contents one can see this, as there are sections titled: I’d like to read this book on Kindle Don’t have a Kindle? Get to Know Us. Some of these items ship sooner than the others. Thus the language that the author employs is informal, and a listing of the best discussions in the book would really entail a listing of every one in the book.
This book would make an excellent supplement to a more formal textbook such as Munkres, but is not a substitute for it.
Customers who viewed this item also viewed. ComiXology Thousands of Digital Comics. Often algebraic topology texts assume that the ianich is well acquainted with arguments of a previous course in point-set topology like this in order not to get trapped on details. Learn more about Amazon Prime.