Basic Topology(Hardback) - 1997 Edition

by M.A. Armstrong

I'm surprised that several previous reviewers have given this book low ratings. This book is far superior to the standard introductions. As someone who has studied topology for several years now, I have found that the greatest failing of many introductory texts is the inability to give a real 'feel' for the subject. By 'feel' I mean not only familiarity with the necessary tools and ways of thought needed to progress to higher levels of understanding but also experience with the kinds of problems that plague(excite?) topologists on a daily basis. Several texts proceed in the logical progression from point set topology to algebraic topology. Munkres is among the best of this style. But the logical order is not always pedagogically best, especially in topology. To start one's topology career by spending one or more semesters on point set topology is utterly ridiculous, given that such point set subtleties are to a large degree not used to study the beginnings of geometric or algebraic topology. This is how these texts fail to give students the 'feel' for topology; the student has no idea what it is that most topologists do, and in fact will not get a good idea until much later. Armstrong tries (and succeeds for the most part) in grounding concepts in real applications, the way the tools are actually used by research mathematicians. Perhaps this is part of why it may be confusing to the novice; introducing topological groups and group actions on spaces right after the section on quotient spaces may appear a bit much, but those concepts are a big part of *why* quotient spaces are so important! Incidentally, the material on quotient spaces is the most complete I've ever seen in an introductory book; Armstrong covers cones and also gluing/attaching maps.

Genres: Mathematics, Reference, Science, Nonfiction, Geometry

Hardcover

First published January 1, 1979

Reviews

[Gavin · Rating 2 out of 5]

This book was my Moral Equivalent of War (in the sense of William James) ... basically, it made me the man I am today by revealing in ridiculous desperation my intellectual and emotional frontiers through my ultimately self-flaggelating perseverence. I believe this book gave me PTSD. Highly recommended for 1) smart people, I mean, really smart; and 2) complete idiots. This book taught me that I cannot even prove that I am not a mathematician.

[Jialin · Rating 4 out of 5]

The author is a typical geometrical mathematicians who is really good at intuitive imagination. However, I am not so sensitive to geometry but prefer analysis and algebra. So when I saw another classical textbook by Munkres, I thought that may be better for learners who lack strong intuitive imagination about geometry.
Even though, this is a great topological textbooks for undergraduate mathematical students, I personally suggest that readers enforce the intuitive imagination about geometry might find it helpful to review the first chapter after finishing the whole book

[Hannah Thomas · Rating 3 out of 5]

Can I say how..."sloppy" this book is written? If you read this on your own, you will need to have a "guide" or use this as a textbook (which I recommend you use this as) because Armstrong expects you to know even the simplest details. There are a few areas in here that you do need to work out on your own and you do run into a few stumbles that are tricky. There are details in here that need to be clarified, just of how, again, this is written.

[Izzy · Rating 2 out of 5]

This book made me hate topology. Hardest class I've ever taken and I don't think it needed to be that hard and this book was part of why it was so bad. Proofs were handwavey and assume you have great geometric intuition, which I don't.

[Chris · Rating 5 out of 5]

This book takes some maturity to work through all the problems, so I struggled, but I found it very rewarding.

[Simona · Rating 5 out of 5]

I am in no position to judge this book, but what I know is that it has a lot more explanatory paragraphs about motivations, then most textbooks.

[Mohamed Ehab · Rating 4 out of 5]

There is nothing basic about it tbh.

[ER!S · Rating 3 out of 5]

wayyyyyy too condensed for an undergraduate. many key ideas are introduced in the exercises and never explained in the text. you're much better off reading something written in the last 10 years

[Christian Chapman · Rating 3 out of 5]

This book rid me of the sense I was missing insight for not knowing any algebraic topology. I don't regret putting the effort in, and as far as I know it was the path of least resistance to this. I was interested in Janich for this purpose but avoided it since it has no exercises.

The second half of the book is on simplicial homology which, in principle, keeps objects concrete. Some explanations didn't work on me: in spite of examples, I couldn't develop a picture of the simplicial approximation theorem through the explanation given. The book would likely be great with an instructor but I didn't have that luxury. Exercises and sections are uneven in importance and difficulty. Some I found to be impossible. The last section doesn't make sense without knowing some commutative algebra words (I didn't know them).

The open source solution manual may as well not exist: I found a severe, obvious, irreparable errors every time I consulted it. Some true/false questions are even answered wrong with false justification.

[Geoffrey Lee · Rating 3 out of 5]

The title to this book is awfully deceptive. While the material it cover's is indeed "Basic Topology", the book makes it anything but "Basic". There are errors in the text and the homework problems are ridiculously challenging for a book which is supposed to be a "first exposure" on the subject. In fact, the title of the book can be questioned as to whether or not the content is truly "basic". In addition to covering the fundamental group and the classification of covering spaces, the book also covers basic homology theory which more advanced books such as Munkres and Massey's Algebraic topology leave out. While the author only restricts his attention to the more basic case of simplicial homology, some of the power and elegance is lost without presenting the more general and powerful theory of singular homology. In my opinion, it is a mistake to present homology theory without covering exact sequences and excision (as the reader is left to feel that the computation of such invariants is very ad-hoc and "messy").

[Le Lai]

good

[Chayan Jain · Rating 5 out of 5]

GUD BOOk

[tyler · Rating 1 out of 5]

loathsome, terrible book

[ali]

informatin about topology