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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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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.

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 topologg introductory text intended for topologyy.

Dignaga 2 5. Topology Undergraduate Texts in Mathematics by K. I’d like to read this book on Kindle Don’t have a Kindle?

Topology : Undergraduate Texts in Mathematics

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. Learn more about Amazon Prime.

Customers who bought this item also bought. Quotient spaces,homotopy, complexes and urysohn and tietze lemma along with partitions of unity are tackled next. This has to rank as one of the best paragraphs that has every appeared in a mathematics book, for it nicely summarizes the need for developing a feel for the concepts behind mathematics before moving on to the rigorous proofs.

Unless you are taking something on faith on purpose, but I get the feeling that is not your intent here, but rather you want to understand the material. One point is that the argument mixedmath is giving is something that is directly verifiable at the point-set level.


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

Topoology 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. You will take away so much for the price paid. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. 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.

Basic Topology Undergraduate Texts in Mathematics. Pages with related products.

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I imagine that I’ll be more slick and fast as I gain more experience, since I’ll know the patterns of arguments. Or, closer to topology, I could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere.

Concepts are often used before they are defined, or are not defined precisely, topologj is liable to frustrate these students as well. Third Edition Dover Books on Mathematics.

It is not too often that a book about topology is written with the goal of actually explaining in detail what is going on behind the formalism. Get to Know Us. As long as it is backed by the gold standard of rigorous proofs, the paper money of gestures is an invaluable aid for quick communication and fast circulation of ideas. Shall we then abandon all intuitive arguments? But, should I be feeling uncomfortable? Get fast, free shipping with Amazon Prime. Basic topological concepts of open, closed, continuous, product topology, connectedness,compactness and intro to separation axioms is presented in a logical concise and easy to understand way.


You just have to remember what the topology is defined as for quotient spaces, etc. Anyway, I read Hatcher only a few months hanich to study for a qualifying exam. The question of what constitutes a proof has constantly been questioned and revised since the beginnings of mathematics in the Ancient World. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Topology : K Janich :

Home Questions Tags Users Unanswered. For the wealth of examples e. Add all three to Cart Add all three to List. Top Reviews Most recent Top Reviews. Customers who viewed this item also viewed. Sometimes in mathematics it is difficult to see the forest for the trees. Shopbop Designer Fashion Brands.

I might be misinterpreting you, but I think that you are saying that you do not like my suggestion that cell-complex quotients are immediately viewed as a wedge sum of n-spheres. See and discover other items: Set up a giveaway. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers.

For the same reason, intuitive arguments have I would even say crippled the topokogy at which I could otherwise read texts, which I understand is the opposite of what most people would say.

This text gives the reason behind many advanced topological concepts and tantalizes the reader with it’s varied applications. Counterexamples in Topology;Dover Books on Mathematics. Half of the chapter on homotopy is actually concerned with categories and functors, probably not the best way to introduce the subject.

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