When is $\frac{f}{g}$ uniformly continuous? I guess I'm asking this for a better understanding of the concept. I know that if $f,g:D\rightarrow\mathbb{R}$ are uniformly continuous with D a bounded interval, then $fg$ is uniformly continuous. But what assumptions would I need that would allow me to show that $\frac{f}{g}$ is uniformly continuous on $D$?
I would assume that I would have to suppose that $g(x)\ne0$ $\forall$ $x\in D$. Is it really that simple?

If $D$ is compact this is all you need, as any continous function on a compact set is uniformly continous. Otherwise i don't think there is much you can say if all you know is $g\neq 0$. For example consider $D=(0,1)$ $f=1$ and $g=x$. This is not uniformly continous.
