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Math Help - uniform continuity

  1. #1
    Junior Member
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    uniform continuity

    if f and g are 2 uniformly continuous functions on X --> R

    show that f+g is uniformly continuous on X


    I tried showing that f+g is Lipschitz because all Lipschitz functions are uniformly continuous.

    So i end up with d(x_1,x_2) < delta then d([f(x1)+g(x1)],[f(x2)+g(x2)])<epsilon. how can I show this is lipshcitz
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Having \left| (f+g)(x)-(f+g)(x') \right|\le \left| f(x)-f(x') \right|+\left| g(x)-g(x') \right|, the conclusion follows.
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