Are the Unit Ball and Any other Ball Topologically Equivalent How would I correctly show that the unit ball $B(0,1)\subset \mathbb{R}^n$ and the ball $B(a,r) \subset \mathbb{R}^n$ are Topologically Equivalent?
I know I need to find a one-to-one function $f: X\rightarrow Y$ for which $f$ and $f^{-1}$ are both continuous to prove it is Topologically Equivalent; however, I am having a hard time finding such a function. 
A function that came to mind is the equation of a circle or sphere. But I wouldn't know if that's correct.
I want to thank you for taking the time to read this question. I greatly appreciate any assistance you provide

Send $\vec{x}$ to $r\vec{x}$ to stretch the unit ball into a ball of radius $r$. Then translate.  So, your function $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ could be $f(\vec{x})=r\vec{x}+\vec{a}$.  The inverse would then be $f^{-1}(\vec{x})=\frac{1}{r}(\vec{x}-\vec{a})$.
