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Conceptual Topology & Manifolds books

  • Thread starter Winzer
  • Start date
  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
708
7
This is the closest thing I can think of is "The Shape of Space":

https://www.amazon.com/dp/0824707095/?tag=pfamazon01-20

Most of the material in point-set Topology is very abstract and often non-intuitive. I doubt you will find a "conceptual" book that "steps through fundamental theorems" because you really need the proofs to get anywhere.
 
  • #3
xristy
Gold Member
116
2
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.
 
  • #4
1,765
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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Another thing you might try is to look at historical references.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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