Let $D^n=\{x\in \mathbb{R}^n : ||x||\le 1\}$ the unit closed ball in dimension $n$, and $I=D^1=[0,1]$.
We have $D^1\times D^1=I\times I\cong D^2$.
Is it true that
$D^n\times D^m\cong D^{n+m}$
for all $n,m\ge 0$ ? If so, where does the homeomorphism comes from ?