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Math Help - f/g if both are uniformly continuous

  1. #1
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    f/g if both are uniformly continuous

    Is it true or false that for any two uniformly continuous functions f and g on a set D such that g(x)=/=0 on all of D the function f/g is uniformly continuous on D? If yes, prove, if not show a counterexample. What if D is compact?

    Thanks!
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  2. #2
    Senior Member roninpro's Avatar
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    How about f(x)=1 and g(x)=x, defined on (0,\infty)? Those two functions are uniformly continuous, but the function f(x)/g(x)=1/x is not.

    For the second question, you should ask yourself if there are any properties for continuous functions on compact sets.
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