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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So allow me to clarify. Is this level of rigour acceptable? 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: Or a simple closed curve in a plane ‘clearly’ partitions it into two disjoint parts.
The book also covers both point-set topology topological spaces, compactness, connectedness, separation axioms, completeness, metric topology, TVS, quotient topology, countability, metrization, etc.
Write a customer review. You just have to remember what the topology is defined as for quotient spaces, etc. Read more Read less.
Understanding Analysis Undergraduate Texts in Mathematics. Anyway, I read Hatcher only a few months ago to study for a qualifying exam.
Topology : Undergraduate Texts in Mathematics
Topology Undergraduate Texts in Mathematics by K. But I would still consider this as a must-read for all those students who plan on studying mathematics in graduate school. AmazonGlobal Ship Orders Internationally.
Share your thoughts with other customers. At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: Whenever I feel that I am just grinding away jahich technical results, this is one of the books I return to for a little perspective. The book is packed with revealing illustrations and motivations.
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The question of what constitutes a proof has constantly been questioned and revised since the beginnings of mathematics in the Ancient World. Customers who viewed this item also viewed. See all 6 reviews.
Topology : K Janich :
Get to Know Us. I am taking a course in Algebraic Topology. Just for the sections on Urysohn’s Lemma, Tietze’s Extension, and Tychonoff’s Theorem alone this book is worth owning – it contains the nicest proofs of these theorems I have ever seen.
Amazon Advertising Find, attract, and engage customers. Sometimes in topolovy it is difficult to see the forest for the trees. 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. I almost always just tune out when people offer me their intuitions, and develop my own, for this reason.
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. 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:.
The down side topologj this approach is that it completely disconnects the subject manich it’s geometric roots and it becomes simply another branch of algebra whose roots are utterly mysterious.
Second Edition Dover Books on Mathematics. 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.
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Amazon Second Chance Pass it on, trade it in, give it a second life. One point is that the argument mixedmath is giving is something that is directly verifiable at the point-set level.