Let C (JR) denote the set of all continuous functions from JR to R Prove that C (JR) is

Chapter 25, Problem 25.16

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Let C (JR) denote the set of all continuous functions from JR to R Prove that C (JR) is a subring ofthe ring F = M(JR) in Example 24.5. Which properties of continuous functions are required?What happens if C (JR) is replaced by the set of differentiable functions from JR to JR?

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