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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Of course your right. I especially enjoyed the section on covering spaces with which it concludes.

Just for the sections on Urysohn’s Lemma, Tietze’s Extension, and Tychonoff’s Theorem alone this janihc is worth owning – it contains the nicest proofs of these theorems I have ever seen. Undergraduate Texts in Mathematics Hardcover: Well said, although the thing I really don’t like about intuitive handwaving is that intuition differs from person to person.

Topology : K Janich :

Or, closer to topology, I could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere. Counterexamples in Topology;Dover Books on Mathematics. Often algebraic topology texts assume that the reader is well acquainted with arguments of a previous course in point-set topology like this in order not to get trapped on details.

The text is useful to all students of mathematics and physics alike. See all 6 reviews.

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. Another example is the proof? The level of rigor that is needed depends on your own taste. This is definitely the most fleshed-out part; if only the rest of the topoligy could go into this depth. Perhaps the single best accolade I can give the book is that it gives one inspiration and motivation to explore in greater detail mathematical objects discussed.


For the same reason, intuitive arguments have I would even say crippled the speed at which I could janch read texts, which I understand is the opposite of what most people would say. English Choose a language for shopping. Amazon Drive Cloud storage from Amazon. Amazon Renewed Refurbished products with a warranty.

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

Third Edition Dover Books on Janiich. Concepts are often used before they are defined, or are not defined precisely, which is liable to frustrate these students as well. This book would make an janicch supplement to a more formal textbook such as Munkres, but is not a substitute for it. At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: I topologh 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.

Topology : Undergraduate Texts in Mathematics

Mathematics Stack Exchange works best with JavaScript enabled. Top Reviews Most recent Top Reviews. See and discover other items: If you are a seller for this product, would you like topoloogy suggest updates through seller support? I think you’ll notice most of Hatcher’s arguments would pass this test,even if it would probably take a considerable amount of spade work jabich make them completely rigorous in the same sense as a real analysis or algebra proof. This is the most pleasurable text on general topology you are likely to find.


ComiXology Thousands of Digital Comics. The German mathematician Klaus Janich has a wonderful response to this question in his book on topology, which is intentionally very non-rigorous and intuitive: I feel uncomfortable with the proofs Hatcher gives. Would you like to tell us about a lower price?

Shall we then abandon all intuitive arguments? I’d like to read this book on Kindle Don’t have a Kindle? Second Edition Dover Books on Mathematics. The reader will walk away with an appreciation of the idea that topology is just not abstract formalism, but has an underlying intuition that is rich in imagery. There was a problem filtering reviews right now.

This text gives the reason behind many advanced topological concepts and tantalizes the reader with it’s varied applications. Sign up using Email and Password. We are using Hatcher as a textbook. The author does a brilliant job of teaching the reader the essential concepts of point set topology, and the book is very fun to read.

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