Question: Let f E 130/, W) and g E C(W', V). Suppose that there is some it E V, x 5-5 0, with g(f(x)) = x.

Let f E 130/, W) and g E C(W', V). Suppose that there is some it E V, x 5-5 0, with g(f(x)) = x. a) Show that x) 9': 0. (hint: Assume that f(x) = 0, and nd a. contradiction.) b) Show that there is some y 6 W, 3' 95 0, with f{g(y)) = y. (hint: Apply f to the rst equation1 and try and deduce a. suitable y.)

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