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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Email Required, but never shown. Top Reviews Most recent Top Reviews. Anyway, I read Hatcher only a few months ago to study for a qualifying exam. Or, closer to topology, I could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere. At the end of chapter three, which deals janicch the quotient topology, the author writes the following paragraph: 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.
One point is that ropology argument mixedmath is giving is something that is directly verifiable at the point-set level. 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 this manner.
Topology : K Janich :
AmazonGlobal Ship Orders Internationally. This is due to both a frequent lack of precision or formality in proofs and definitions coupled with a tendency to discuss much more advanced material with which a student at this level wouldn’t be familiar.
There is indeed much that is wise in this quote and it really gives what I think is an excellent nanich 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: Basic topological concepts of open, closed, continuous, product topology, connectedness,compactness and intro to tkpology axioms is presented in a logical concise and easy to understand way.
It is often said against intuitive, spatial argumentation that it is not really argumentation,but just so much gesticulation-just ‘handwaving’. Unless you are taking something on faith on topolgoy, but I get the feeling that is not your intent here, but rather you want to understand janch material. Basic Topology Undergraduate Texts in Mathematics. 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 an introductory text intended for undergraduates.
Of course, as it’s stated, this isn’t an exact science.
Some of these items ship sooner than the others. Understanding Analysis Undergraduate Texts in Mathematics. The details of the questions you asked can be diligently unwound.
Sign up using Facebook. But I would still consider this as a must-read kanich all those students who plan on studying mathematics in graduate school. Shall we then abandon all intuitive arguments? 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. Please try again later.
Quotient spaces,homotopy, complexes and urysohn and tietze lemma along with partitions of unity are tackled next. So allow me to clarify. Also, Lagrange’s theorem is also immediate in your sense because quotienting a finite group by a subgroup is precisely the collapsing of its cosets to a point, so clearly the number of elements in the quotient is exactly the number of cosets. I’d like to read this book on Kindle Don’t have a Kindle? But I think Janich has given some quite good advice janixh the novice here.
Half of the chapter on homotopy is actually concerned with categories and functors, probably not the best way to introduce the subject. The text is useful to all students of mathematics and physics alike. Third Edition Dover Books on Mathematics. This is definitely the most fleshed-out part; if only the rest of topplogy book could go into this depth.
Topology : Undergraduate Texts in Mathematics
I am taking a course in Algebraic Topology. Alexa Actionable Analytics for the Web. 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. Share your thoughts topolovy other customers. However, too much material is mentioned that is certainly over the heads of most students new to topology, such as the Pontrjagin-Thom construction, the spectrum of commutative Banach algebras, or Lie groups, often in a very cursory manner that would serve only to confuse beginners.