Authors Authors and affiliations L. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Personalised recommendations. Cite chapter How to cite? ENW EndNote. Buy options. The students learn the concepts fast, their theoretical language to explicate honed, and their visualization skills improved. From chapter 5 and on it provides one of the most modern theoretical works in Topology and group theory and their inter-relationships.
245B, Notes 8: A quick review of point set topology
The exercises are superbly chosen and the examples are wonderful in pushing the theory forwards. Both the language and presentation are modern and allows for much room for visualization computational development. This book is excellent for visualization and at the same precise theoretical treatment of the subject. I do not recommend Munkres I work with both his books on manifolds and topology and the students did not grasp much of the theory.
The presentation is old and tired. I'm assuming that the students are not familiar with point-set topology and it's the first course in topology for them. I'd recommend a combination of Munkres and Intuitive topology by V. There will be a great deal of precision and intuition all together. A book that I find very readable is "Topology" by John G. Hocking and Gail S. I have little teaching experience, but I remember being a student and based on that I believe that a few years ago I would have also liked this book.
I am an undergraduate student. I think that when you begin to study a new subject it is better to start from books not too broad.
For a basic course in topology, I recommend these books based on my experience as student. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. A book in topology Ask Question. Asked 7 years, 9 months ago. Active 5 years, 10 months ago.
Viewed 14k times. In the past I have used two different books: Elementary Topology. Textbook in Problems, by O. Viro, O. Ivanov, V. Kharlamov and N.
A Course in Point Set Topology : John B. Conway :
Any suggestions? It covers all the usual point set topology and some dimension theory. Although the second part of the book dealing with Algebraic Topology is not as good as other specialized books in AT such as Hatcher's book which is free to download on Hatcher's site.
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What have they seen and not seen yet? Crossley does not think that fundamental group could be the highest point in the course. Nevertheless, this is the best answer I have got so far. Thank you very much. Michael Biro. It's nice to get used to his writing style early. Today, yet another question was posted on Math. Stackexchange this time by the new user avatar asking for topology references. This has been asked a few times before, but somehow the answers are a little bit different.
To be clear, this is a compilation of much not all of the discussion in the following questions and their answers : best book for topology? And I insert my own thoughts and resources, when applicable. Ultimately, this is a post aimed at people beginning to learn topology, perhaps going towards homology and cohomology rather than towards a manifolds-type, at least for now.
One cannot mention references on topology without mentioning Munkres Topology. In fact, Munkres once said that he explicitly wrote his book to be an accessible topology book to undergrad. If the goal is to immediately go on to learn algebraic or differential topology, some think that the first three chapters of Munkres is sufficient.
Munkres serves primarily to give an understanding of the mechanics of point set topology.
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The user Mathemagician says in a comment that it is practically the Bible of point-set topology, and extremely comprehensive. In a comment on a different thread, Brian M. Sean Tilson wrote up an answer discussing Willard as well. In short, he thinks it is superior to Munkres, but that it is necessary to do the exercises to learn some key facts.
Table of contents
In Munkres, this is not the case, but one needs to do exercises to develop any sort of intuition with Munkres. I know many people who learned point set from Armstrong rather than Munkres. I have personally only cursorily glanced through Armstrong, and I found it roughly comparable to Munkres. When I read the reviews on Amazon for Munkres and Armstrong , however, there is a strange discrepancy.
hantycircder.tk Munkres far outscores Armstrong whatever that really means. Perhaps this is due to the recurring theme in the top reviews of Armstrong, which say that Armstrong deviates from the logical and some would say, intuition-less flow of Munkres to instead ground the subject in a diverse set of subjects. On the other hand, this review says that Munkres is simply more extensive. On a different note, there is a freely read but not printed book by S.
Morris called Topology without tears. This is a link to the pdf on his website. I should note that the version linked is not printable. I think this book is very readable, and is perhaps the gentlest introduction text here for better or worse. It comes very highly recommended for those interested in that niche.
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