I need help proving if D is compact, then f/g must be uniformly continuous on D.

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- Apr 20th 2008, 05:32 PMstudent1001[SOLVED] Urgent -f/g need not be uniformly continuous
I need help proving if D is compact, then f/g must be uniformly continuous on D.

- Apr 20th 2008, 05:52 PMTheEmptySet
Unless there are other hypothsis the statement is false

counter example:

let

$\displaystyle D=[1,3] \mbox{ and } f(x)=x,g(x)=3-x$

Both f and g are uniformly cont on D $\displaystyle \epsilon=1$ will work for all delta but $\displaystyle \frac{f(x)}{g(x)} $

I am thinking that $\displaystyle g(x) \ne 0 $ on D as well.