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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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The author then delves into topological groups and vector spaces introducting Hilbert Banach and Janichh spaces albeit briefly. Amazon Second Chance Pass it on, trade it in, give it a second life. Sign up using Email and Password.

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algebraic topology – How much rigour is necessary? – Mathematics Stack Exchange

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 our intuitive argument is a valuable one. Amazon Drive Cloud storage from Amazon. I believe that experienced mathematicians, who perhaps learned point-set topology from books such as those of Munkres, Kelley, or Bredon or even an analysis book such as Roydenappreciate how this book focuses on motivating the concepts, explaining how the various objects are used elsewhere in mathematics – for that purpose this is one of the finest books I have seen.


Explore the Home Gift Guide. I am taking a course in Algebraic Topology. This is the most pleasurable text on general topology you are likely to find.

Well said, although the thing I really don’t like about tpoology handwaving is that intuition differs from person to person. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers.

Thus the language uanich 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.

The level of rigor that is needed depends on your own taste. But since algebraic topology is so closely related to classical geometry, completely abstract reasoning would probably strip away much understanding of the sources of most of the central concepts,which I believe was Hatcher’s reason for writing the text in this manner.

Understanding Analysis Undergraduate Texts in Mathematics. Buy the selected items together This item: This is due to both a frequent lack of precision or formality in proofs and definitions coupled with a tendency to discuss much more advanced material with which a student at this level wouldn’t be familiar. Amazon Advertising Jwnich, attract, and engage customers.

Topology : K Janich :

Add all three to Cart Add all three to List. We are using Hatcher as a textbook. One of the main problems I am facing with the textbook is its level of rigour.

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Please try again later. While I agree with the other reviewers here that Janicch “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.

Topology : Undergraduate Texts in Mathematics

Home Questions Tags Users Unanswered. Certainly this book couldn’t be used as a textbook for an undergraduate course – for the reasons mentioned above and also because not enough material is actually covered, as well as the obvious deficiency in that it lacks exercises for the reader. There is indeed much that is wise in this quote and it really gives 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 point is really proves nothing: Topology Undergraduate Texts in Mathematics by K.

East Dane Ttopology Men’s Fashion. Sometimes in mathematics it is difficult to see the forest for the trees.