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Topology learning recommendations

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This page provides subject-specific learning recommendations for the subject topology. See all our learning recommendations pages |

Basic ideas of point set topology are an important part of undergraduate mathematics education. The most important ideas are covered in an undergraduate analysis course or course sequence. However, a point set topology course typically deals with the ideas at a somewhat higher level of abstraction than the typical analysis course.

For most people, it is recommended that the study of point set topology be deferred until after you have taken an undergraduate analysis course sequence (or done equivalent self-study), because many ideas of topology generalize concepts seen in the analysis sequence. However, if you have a strong background in theoretical calculus and have a strong background with proofs in general (perhaps acquired in the context of contest math) then it may be more efficient for you to self-study point set topology first and then go over the most important theorems in analysis.

Recommendations

Our top general recommendations are recommendations that we would give people if we had to name just a few top books. Our niche recommendations are recommendations that suit learners with specific learning styles or goals. For learners who fit one of the niches, the niche recommendation would be better. Price ranges are provided to give better context to the strength of our recommendation.

Top general recommendations

Book Author ISBN and purchase links Price estimate (may be outdated, and international editions may be cheaper) Who we're recommending it for and why we're recommending it
Topology (2nd Edition) James Munkres ISBN 978-0131816299 , Amazon link Hardcover $100-150, Paperback ~$20 (secondhand, not available firsthand in the US) This is the most standard and likely the best introduction to point set topology. It goes into adequate detail and has clear proofs. A LessWrong comment on the best textbooks says that the book was preferable to other books that cover the subject "intuitively" because the added rigor really is helpful for understanding the subject well.
Introduction to Topology (Second Edition) Theodore W. Gamelin and Robert Everist Greene ISBN 978-0486406800, Amazon link $10-15 This is a cheaper book that covers all the important topics , and may not differ that much from Munkres for the most important subtopics.

Niche recommendations

Book Author ISBN and purchase links Price estimate (may be outdated, and international editions may be cheaper) Who we're recommending it for and why we're recommending it
Lecture Notes on Elementary Topology and Geometry I. M. Singer and J. A. Thorpe ISBN 978-0387902029, Amazon link) $40-70 This book includes a very compact introduction to point set topology in its first two chapters. This is not good as a primary learning source, but if you intend to study higher mathematics, it could be a useful book to read from and be inspired by on the side as you work through either of the above books.