Conceptual Topology & Manifolds books

[Winzer]

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.

 

[Sankaku]

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.

 

[xristy]

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.

 

[homeomorphic]

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Another thing you might try is to look at historical references.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.