Good books to Learn General topology

Question

I am quite interested in learning topology from the basics, I would like to find a book that is quite detailed and has a large number of examples.

What are the best books to easily understand topology?

Thanks.

Munkres uses an appalling notation for ordered pairs, but in most respects it’s the obvious choice. — Brian M. Scott, Nov 20 '20 at 03:31
@BrianM.Scott: I think Munkres sometimes uses $x\times y$ to avoid confusion with the open interval $(x,y)$ — J. W. Tanner, Nov 20 '20 at 04:30
@J.W.Tanner: I’m sure that that’s at least part of his reason, but it’s still an appallingly bad choice, not least because it’s completely idiosyncratic. — Brian M. Scott, Nov 20 '20 at 04:46
Does this answer your question? Best book of topology for beginner? — feynhat, Nov 20 '20 at 08:07

score 3 · Answer 1 · answered Nov 20 '20 at 17:15

3

Gustavo Rubiano's book, introduction to Topology (Victor Anatolyevich Vassiliev).

answered Nov 20 '20 at 17:15

Levi

61

score 2 · Answer 2 · edited Nov 21 '20 at 23:28

2

Munkres is good, or this book: http://www.ehu.eus/~mtwmastm/TG0910.pdf

edited Nov 21 '20 at 23:28

J. W. Tanner

60,406

answered Nov 20 '20 at 15:04

Levi

61

score 1 · Answer 3 · answered Nov 20 '20 at 01:59

1

My recommendations: Elementary Topology: Problem Textbook and Topology without Tears. (Both are available online.)

Stephen Willard's General Topology is also a nice choice.

answered Nov 20 '20 at 01:59

Bernard Pan

2,887

Willard is excellent, though perhaps not the best book for beginners. I don’t at all care for the text at the first link, though I do approve of separating proofs from theorems. I don’t care for the order of topics in Morris’s book, but the book is certainly usable. – Brian M. Scott Nov 20 '20 at 03:30

MISSINGNO · Accepted Answer · 2020-11-25T18:56:57.697

"Topology" by James Dugundji has the best of many worlds: formality and richness in content without being too obnoxious or cryptic for someone who has no idea of topology.

"Topology" by James Munkres is (I think) an excellent introductory book, very digestible and easy to handle. The main drawback I see from this one is that it can be a bit slow, so if you are in a hurry to learn topology go for Dugundji instead.

"General Topology" by Stephen Willard is an excellent book that not only teaches you the concepts, but also the reason behind them. Unfortunately, Willard leaves too much to the reader (for my taste), and it can be a bit lacking in problems.

Last but not least, "Topology" by Ryszard Engelking is somewhat considered a bible among students and teachers. It is an extremely complete book, but it can be a tough read for a beginner. I don't recommend starting with this one, but I wanted to mention it since it can be a good reference in the future.

Unfortunately, I have yet to find THE perfect book for an introductory course to Topology, but I feel that the combination of this four books is an excellent way to dip your toes in topology. My main recommendation is to start with Munkres, if you feel it's too easy and slow go for Dugundji while complementing with Willard, and if everything still feels too basic and obvious, go for Engelking.

All of these are good in their respective ways, but I definitely consider Engelking more a reference work than a textbook. I don’t know Nagata’s Modern General Topology at all well, but it’s another one that is probably worth a look. — Brian M. Scott, Nov 20 '20 at 05:05

Good books to Learn General topology

4 Answers4