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Conceptual Topology & Manifolds books

  1. Apr 15, 2012 #1
    I am looking for books that introduce the fundamentals
    of topology or manifolds. Not looking for proofs and rigor.
    Something that steps through fundamental theorems in the
    field, but gives conceptual explanations.
     
  2. jcsd
  3. Apr 15, 2012 #2
  4. Apr 15, 2012 #3

    xristy

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    Gold Member

    One intuitive book is Griffiths' Surfaces a few theorems such as the Konigsberg bridge problem and the Euler characteristic are demonstrated in simple language along with non-orientable surfaces and so on.

    Crossley's Essential Topology unfortunately includes some proofs but is not big on rigor. I suspect that it will be difficult to find a book that doesn't have some proofs.
     
  5. Apr 16, 2012 #4
    You could try Prasolov's Intuitive Topology. I haven't read it, but I took a look inside and it seems like that sort of thing.

    There's also a book, Algebraic Topology: An Intuitive Approach.

    Armstrong: Basic Topology has an introduction along the lines you have in mind.

    Hilbert and Cohn Vossen's book, Geometry and the Imagination has a chapter on topology.

    Another thing you might try is to look at historical references. It should be kept in mind that the study of topology really precedes point-set topology in its modern form. One of the earliest results was the classification of surfaces by Riemann and Mobius, independently, back in the 19th century. Whereas, I think point-set sort of reached a pretty modern form in the 1920s. Another interesting thing to look at, which I haven't done yet, is to read Poincare's old papers. Also predating point-set.
     
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