Please only use definitions, propositions, theorems given in the book ''Differential Topology'' by Guillemin and Pollack !

And if you refer to a proposition, theorem or exercise in the book please refer to them by chapter and section!

Also please explain each step, even if it seems trivial to you!

Please don't answer this question by using theory that is NOT covered in the book by Guillemin and Pollack!!!! The Propositions and Theorems in the book of Guillemin and Pollack are NOT numbered, so if you end up referring to Propositions by numbers, you are using the WRONG book!

Special Case. Any smooth map f: S' - S' having degree zero is homotopic to a constant map. 4. Check that the special case implies the following corollary. Corollary. Any smooth map f: S' - R/+1 - {0) having winding number Zero with respect to the origin is homotopic to a constant.4. The hypothesis is that the degree of f/| f| is zero, so f/| f | is homo- topic to a constant. But as maps into R*+1 - {0), f and fif | are homotopic