#### quasar987

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Now, in the event that f is a homeomorphism, it follows from the elementary properties of the degree that deg(f)=±1. After this remark, Hatcher adds that in applications, it is usually not hard to determine which it is between +1 and -1.

Can someone give an example illustrating how one decides between +1 and -1?

(2) How to see why the above definition of degree coincide with the one in terms of preimage of regular value in the case of a differentiable f?

Thanks.