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Are there any books on topology which can be read without having to do any exercises and look up definitions every second line? Something to read while relaxing, and not meant to replace a textbook but perhaps accompany one? I'm specifically interested in algebraic topology but that might be too much to ask for.

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  • $\begingroup$ What is your background ? $\endgroup$ – user171326 Jul 7 '15 at 21:32
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    $\begingroup$ I have an graduate degree in physics and am currently reading Lee's topological manifolds $\endgroup$ – terry Jul 7 '15 at 21:33
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    $\begingroup$ I think Lee is an example of book you can read without do too much exercise. But from my point of view you will learn nothing if you don't do exercise or have difficulties with a book. It depends if you want to learn topology, in say 6 months, or if you want to have a quick overview in 2 weeks... Anyway, "Singer and Thorpe, Lecture Notes on Elementary Topology and Geometry" looks to be a good reference for your request. You have also lot of recommandations on this thread : math.stackexchange.com/questions/7520/best-book-for-topology $\endgroup$ – user171326 Jul 7 '15 at 21:40
  • $\begingroup$ @N.H. I want both but this question is about the latter $\endgroup$ – terry Jul 8 '15 at 14:43
  • $\begingroup$ A topological picturebook by George Francis? $\endgroup$ – Matthew Towers Jul 8 '15 at 19:21
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Something basic is First Concepts of Topology, a positively reviewed book that is both cheap and short, and it also reads like a narrative (there are exercises if you want to enhance your understanding, but you obviously do not have to do them unless you want--full solutions to the exercises are available in the back of the book).

Perhaps more along the lines of what you are looking for is David Richeson's Euler's Gem: The Polyhedron Formula and the Birth of Topology, a very positively reviewed book (and winner of the 2010 Euler Prize by the MAA) where you do not have to do any exercises or constantly look up definitions. From the most helpful review from the link:

If you wanted a popularized book-length treatment of topology before Dave Richeson's Euler's Gem: The Polyhderal Formula and the Birth of Topology, you had no choice at all.

I'd highly recommend Euler's Gem, but it is longer than the first book and it is also more expensive; nonetheless, it is a book you could probably enjoy rather easily (i.e. it is something to read while relaxing and definitely something good to accompany a textbook if you want).

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Introduction to Topology. Pure and Applied by C Adams & R Franzosa

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  • $\begingroup$ you could be a bit more descriptive... $\endgroup$ – JMP Jul 25 '15 at 5:39

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