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## Direction of a vector field

Let $${ f: S^n \rightarrow S^n }$$ be a map of degree zero. Show that there exists points $${ x, y \in S^n }$$ with $${ f(x) = x }$$ and $${ f(y) = – y}$$. Use this to show that if F is a continuous vector field defined on the unit ball \({ D^n […]