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# Dense Subset, Continuity and Uniform Convergence : Let E C R1 and let D be a dense subset of E. If are continuous real-valued functions on E for n=1,2,..., and fn converges uniformly on D, prove...

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Let E C R1 and let D be a dense subset of E. If are continuous real-valued functions on E for n=1,2,..., and fn converges uniformly on D, prove that fn converges uniformly on E.

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I am using the book Methods of Real analysis by Richard Goldberg.

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Dense Subset, Continuity and Uniform Convergence are investigated. The solution is detailed and well presented.

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4.
Let and let D be a dense subset of E. If are continuous real-valued functions on E for n=1,2,..., and converges uniformly on D, prove that converges uniformly on E.

Proof: ...

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