Show that the open unit disk in $\mathbb{R}^2$ is homeomorphic to $\mathbb{R}^2$ I have already perused this answer to a similar question but I still am unsure how exactly they went about proving it is a bijection. Would someone be able to elaborate? Also, how does one come up with the function $\frac{x}{1+||x||}$ to begin with? Thanks.

HINT: Try to find the inverse. I guess the idea was to generalize $f(t)=\frac{t}{1+|t|}$ for higher dimensions.
