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hello, I need a book where i can find the proof for the classification of 1-dimensional topological manifolds. (i already have Milnor's for the classification of 1-dimensional smooth manifolds) thank you

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What you need is the existence of a unique smooth structure (if it exists) on a 1-dim topological manifold. – David Roberts Jan 9 '11 at 8:30
up vote 3 down vote accepted

If I remember well, Introduction to topological manifolds (Lee) proves the classification theorem for 1-dim manifolds.

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Fuks, D. B.; Rokhlin, V. A. Beginner's course in topology. Geometric chapters. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin-New York, 1984.

For dim 1 and dim 2 manifolds.

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