(1) For a continuous map f:S^n-->S^n, the induced map in top homology is, up to identification of H_n(S^n) with Z, just multiplication by an integer, and this integer is defined as the degree of f. (in Hatcher: http://www.math.cornell.edu/~hatcher/AT/ATpage.html) 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.