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 closest anyone’s ever come to pulling it off to me is Rotman. Of course, as it’s stated, this isn’t an exact science.
Topology : Undergraduate Texts in Mathematics
As for the larger question of how much rigor is necessary, I think a proof should contain enough rigor to provide a high-level sketch of how one would create a mechanically checkable proof, given enough time and energy. East Dane Designer Men’s Fashion. Showing of 6 reviews. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. It ttopology often said against intuitive, spatial argumentation that it is not really argumentation,but just so much gesticulation-just ‘handwaving’.
Get to Know Us. See all 6 reviews. 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: Jeff 3, 1 12 Learn more about Amazon Giveaway.
Shall we then abandon all intuitive arguments? You will take away so much for the price paid. This text gives the reason behind many advanced topological concepts and tantalizes the reader with it’s varied applications. 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.
Sign up or log in Sign up using Google. 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.
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It is not too often that a book about topology is written with the goal of actually explaining in detail topologt is going on behind the formalism. 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. See and discover other items: The details of the questions you asked can be diligently unwound. For the same reason, intuitive arguments have I would even say crippled the speed at which I could otherwise read texts, which I understand is the opposite of what most people would say.
The book also covers both point-set topology topological spaces, compactness, connectedness, separation axioms, completeness, metric topology, TVS, quotient topology, countability, metrization, etc. Janixh by looking at the contents one can see this, as there are sections titled: Pages with related products. For the wealth of examples e. Customers who viewed this item also viewed. But I think Janich has given some quite good advice to the novice here.
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 topologj for the reader.
Home Questions Tags Users Unanswered. Ask if you need help. Counterexamples in Topology;Dover Books on Mathematics. One of the main problems I am facing with the textbook is its level of rigour. There’s a problem loading this menu right now. Amazon Rapids Fun stories for kids on the go.
Topology : K Janich :
Add all three to Cart Add all three to List. Topology Undergraduate Texts in Mathematics by K. Half of the chapter on homotopy is actually concerned with categories and functors, probably not the best way to introduce the subject.
Understanding Analysis Undergraduate Texts in Mathematics. Amazon Music Stream millions of songs. The book is packed with revealing illustrations and motivations. While this is intuitively clear, it requires some work to prove. Email Required, but never shown. Please try again later. Explore the Home Gift Guide. 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:.
English translation Original Language: Is this level of rigour acceptable?
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. The level of rigor that is needed depends on your own taste.
Anyway, I read Hatcher only a few months ago to study for a qualifying exam. Shall we then abandon all intuitive arguments? Perhaps the single best accolade I topolkgy give the book is that it gives one inspiration and motivation to explore in greater detail mathematical objects discussed.