Does there exist a bijective mapping $f: \Delta\to\mathbb{C} $ Does there exist a bijective mapping $f: \Delta\to\mathbb{C} $?
Yet I have not found such example. Is it false (why?),please help me.
$ \Delta $ is the unit disk in $\mathbb {C}$.

I would do this radius by radius. So in case we were talking about the open disk, all we’d need to do is get a nice map from $[0,1\rangle$ onto $[0,\infty\rangle$, like $x/(1-x)$. In case we were talking about the closed disk, you need a (discontinuous) map from $[0,1]$ onto $[0,1\rangle$, and follow it by the map you chose before. For this discontinuous map, one might send $1/n$ to $1/(n+1)$ for all $n\ge1$.
