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Math Help - Equicontinuity implies Uniform Equicontinuity

  1. #1
    Junior Member
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    Equicontinuity implies Uniform Equicontinuity

    Let A be a equicontinuous subset of C(X,F). Show that A is Uniform equicontinuous, ie:



    $\[\forall \varepsilon  \succ 0,\exists \delta  \succ 0/{\left\| {f(x) - f({x_0})} \right\|_F} \prec \varepsilon ,\forall f \in A,\forall x,{x_0} \in X,d\left( {x,{x_0}} \right) \prec \delta \]$

    Please help me, I have a test tomorrow.

    Regards

    Felipe
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  2. #2
    Senior Member Tinyboss's Avatar
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    It's not true as stated. For example, let A={f}, where f is not uniformly continuous. Are you sure you didn't leave out any hypotheses?
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