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Math Help - More Real Analysis: Epsilon-Delta: Uniformly Continuous

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    More Real Analysis: Epsilon-Delta: Uniformly Continuous

    Another question, sorry Final Friday, senior year, this class is horrible

    Let f: D-->R be uniformly continuous on D and let cED. Prove using an
    epsilon-delta argument cf is uniformly continuous on D.

    R = Real Numbers
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    Quote Originally Posted by Vitava61 View Post
    Another question, sorry Final Friday, senior year, this class is horrible

    Let f: D-->R be uniformly continuous on D and let cED. Prove using an
    epsilon-delta argument cf is uniformly continuous on D.

    R = Real Numbers
    let \epsilon > 0
    Since f is uniformly continuous there exisits a delta for every epsilon such that

    |x-y|< \delta |f(x)-f(y)|<\frac{\epsilon}{|c|}

    Now for |x-c|< \delta

    |cf(x)-cf(y)|=|c||f(x)-f(y)|<|c|\cdot \frac{\epsilon}{|c|}=\epsilon

    QED
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