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Topology Topology book for self-study

  1. Feb 24, 2017 #1
    Hi,

    I would like to receive suggestions regarding (general) topology textbook for self-study.
    I have background in real analysis, linear and abstract algebra. I am not afraid of a challenging book.

    Thank you!
     
  2. jcsd
  3. Feb 24, 2017 #2
  4. Feb 24, 2017 #3
  5. Feb 24, 2017 #4

    MathematicalPhysicist

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    Munkres.
    If you want a challenge then try to prove the theorems in it before reading Munkres' treatment.
     
  6. Feb 24, 2017 #5
    Seconded on Munkres, if your background is pretty solid and you don't feel you need a lower level primer. Munkres is the wiz and nobody beats him!

    In the introduction he gives good possibilities for course outlines if you want to skip nonessential material on your first pass.
    -Dave K
     
  7. Feb 24, 2017 #6
    Thank you both for the recommendation. Is it crucial to get the second edition, or the first is as good as the second?

    Thank you!
     
    Last edited: Feb 24, 2017
  8. Feb 25, 2017 #7
    I strongly recommend "General Topology" by Ryszard Engelking, which is regarded as a BIBLE by many set-theoretic topologists. If you read this book, you practically mastered the topology. If you want to learn the basics of general topology, differential topology, and algebraic topology, I recommend "Lecture Notes on Elementary Topology and Geometry" by Singer or "Topology: A Geometric Approach" by Engelking.
     
  9. Feb 25, 2017 #8
    Thank you for the recommendation. Are any of these books suitable for self study?
    Thank you.
     
  10. Feb 25, 2017 #9

    MathematicalPhysicist

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    @bacte2013 it
    No one really master topology or any other field in maths; there's always more to be learnt.
    But perhaps after reading Engelking one can turn to read books like the handbook by Kunnen on set theoretic topology.
     
  11. Feb 25, 2017 #10
    Well, it is considered that one learned every possible topics in the undergraduate- and graduate-level in general and set-theoretic topology after reading Engelking. Have you read Engelking? Not only it covered all topics, including ones currently searched, in the general and set-theoretic topology. Of course, one can learn specific topics in-depth, but the book provides all general information and conjectures in the topology.

    After reading Engelking, you practically do no have to read any other books in topology, but can jump right into research papers. Surprisingly, all current research in the set-theottic topology are included in his book.

    Kunen's book you mentioned is an extension of some specific topics in the Engelking.
     
  12. Feb 25, 2017 #11
    If you are willing to put a lot of time and your have a basic understanding of proof techniques, yes by all means! Since you took real analysis, you are more than ready! If you would like to learn basic overviews of the different branches of topology, but not in great depth, I recommend other two books I mentioned after Engelking. If you read Engelking, you practically do not have to pick up other books in the general or set-theoretic topology, and you can jump right into research papers.

    If you are interested in the algebraic topology, I recommend those later two books I mentioned and Spanier's Algebraic Topology.
     
  13. Feb 25, 2017 #12

    MathematicalPhysicist

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    No I haven't read Engelking, I read Munkres but didn't finish it; I read it for the undergraduate course in topology which I took in my BSc.

    I must find the time to read both books, I quite like topology. (it's hard time reading so many books in maths,physics,engineering and logic; I must be patient, everything will come in due time).
    Cheers! good learning to all!
     
  14. Feb 25, 2017 #13

    MathematicalPhysicist

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    @bacte2013 I remember reading in MSE or is it overflow, that not even Edwin Spanier taught from his book his classes in algebraic topology.
    :-)
     
  15. Feb 25, 2017 #14
    Thank you very much. I'll check these books and hopefully will help. I really liked the abstract algebra, but have no idea how it is combined in topology. Sounds interesting indeed.

    Thank you all!
     
  16. Feb 26, 2017 #15
    Munkres. Munkres. Munkres.
     
  17. Feb 26, 2017 #16
    I place Engelking's two books and Singer/Thorpe above Munkres. Engelking covers so many topics in the general topology in details, and has gazillions problems and conjectures with original papers to read. Singer/Thorpe and Engelkin's another book provides really good introduction to the algebraic and differential topology enough to read books like Spanier and Do Carmo.
     
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