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Let C(R, R) be the space of continuous functions from R to R. It is easy to see that C(R, R) is a vector space (with operations and defined in natural way). Check if each of the following subsets is a subspace of C(R, F (a) S = Cl (R,R)-the space of differentiable functions from R to R (b) s-{f є C(R, R) : If(x) _ f(y)1 KM- } 、〈|x This space is called space of Hölder continuous functions of exponent/order 1/2 _ ?/ for some constant K

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