Question: Let W be a non-empty, connected topological space. Let : W W be a continuous map such that 4 (w) = w for all w

Let W be a non-empty, connected topological space. Let : W W be a continuous map such that 4 (w) = w for all w W. If f : W R is a continuous function, show that there exists w0 W with f(w0) + f( 2 (w0)) = f((w0)) + f( 3 (w0)).

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