Prove that if K in the complex plane is compact and f(z) and g(z) are uniformly continuous functions on K, then f(z)g(z) is uniformly continuous on K.
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Originally Posted by grad444 Prove that if K in the complex plane is compact and f(z) and g(z) are uniformly continuous functions on K, then f(z)g(z) is uniformly continuous on K. Since f amd g are continous on K so is f*g. But since f*g is continous on a compact set it is automatically uniformly continous.
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