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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Topology : Undergraduate Texts in Mathematics
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. 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.
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.
In fact, here is direct quote from the index: Third Edition Dover Books on Mathematics. 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.
Counterexamples in Topology;Dover Books on Mathematics. Or, closer to topology, I could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere.
The level of rigor that is needed depends on your own taste. Physicists in particular, who must assimilate mathematics very quickly in order to apply it to real problems must have a pictorial, “playful” understanding of the mathematical constructions. 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.
Sign up using Facebook. There topolovy indeed much that is wise in this quote and it manich gives what I think is an excellent “rule of thumb” for determining when a “proof” janjch mathematics has crossed the line and really become non-rigorously vague by 21st century mathematical standards to the point is really proves nothing: I believe that experienced mathematicians, janicg 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 ajnich – for that purpose this is one of the finest books I have seen.
Many topics are given such short attention it makes you wonder why the author even bothered – such as a page devoted to Frechet spaces followed by a section consisting of a single paragraph on locally convex topological vector spaces. 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 jaanich on to the rigorous proofs.
English translation Original Language: Is this level of rigour acceptable?
If you are a seller for this product, would you like to suggest updates through seller support? Or a simple closed curve in a plane ‘clearly’ partitions it into two disjoint parts.
Dignaga 2 5. Add all three to Cart Add all three to List. I am taking a course in Algebraic Topology. While this is intuitively clear, it requires some work to prove. The book also covers both point-set topology topological spaces, compactness, connectedness, separation axioms, completeness, metric topology, TVS, quotient topology, countability, metrization, etc.
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algebraic topology – How much rigour is necessary? – Mathematics Stack Exchange
Showing of 6 reviews. Sometimes in mathematics it is difficult to see the forest for the trees. Most of the proofs until the last chapters are of the 1- or 2-paragraph jamich, with some pictures added, although as the book progresses the level becomes increasingly more sophisticated. 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.
This book would make an excellent supplement to a more formal textbook such as Munkres, but is not a substitute for it.
I feel uncomfortable with the proofs Hatcher gives. Just by looking at the contents one can see this, as there are sections titled: Sign up using Jabich and Password. Set up a giveaway. Explore the Home Gift Guide. There is not one part of the book that is not helpful or interesting, and the author delves into many different areas that involve the use of topology. Whenever I feel that I am just grinding away at technical results, this is one of the books I return to for a little perspective.
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Buy the selected items together This item: The author does topollogy brilliant job of teaching the reader the essential concepts of point set topology, and the book is very fun to read. Learn more about Amazon Prime.
Concepts are often used before they are defined, or are not defined precisely, which is liable to frustrate these students as well. 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 topolpgy manner.