Hi,
I'm given a function f and the unit disk (although it could be any region)
and $\displaystyle f \in D(0;1)$
Does the above mean the domain of the function is the unit disk or the codomain?
$\displaystyle f(X)$ is the codomain if $\displaystyle X$ is the domain. Then $\displaystyle f(X) \subset D(0;1)$ would be the correct notation. Using the $\displaystyle \in$ symbol implies that f is a member of a collection of functions not points. In short, I wouldn't call $\displaystyle f \in D(0;1)$ a valid statement (unless in this case, D is a collection of functions, which I've never seen written this way).