Open balls in euclidean space are homeomorphic to the whole space The following question is from Fred H. Croom's book "Principles of Topology"

Prove that each open ball $B(a,r), a\in \mathbb{R}^n, r>0$, considered as a subspace of $\mathbb{R}^n$, is homeomorphic to $\mathbb{R}^n$.

After much studying, I concluded the first way to approach this problem would be by showing that the unit open ball $B(\theta,1)$ with center and radius 1 is homeomorphic to $\mathbb{R}^n$. Afterwards, show how any open ball $B(a,r)$ is topologically equivalent to $B(\theta,1)$, thus ending my proof. However, I am having a hard time showing that $B(\theta,1)$ is homeomorphic to $\mathbb{R}^n$. Any suggestions?

I want to thank you for taking the time to read this question. I greatly appreciate any assistance you provide. 

Hing: Take $B(0,1)$. The let $f(x) = \frac{x}{1-|x|}$.
