Question: If (X, d) is a bounded metric space show that the product of two Lipschitz continuous real-valued functions on (X, d) is again Lipschitz

If (X, d) is a bounded metric space show that the product

If (X, d) is a bounded metric space show that the product of two Lipschitz continuous real-valued functions on (X, d) is again Lipschitz continuous (use the standard topology on R). Give an example to show that this need not follow if X is not bounded.

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