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

By proving $f:B(0,1)\rightarrow B(a,r)$ defined by $f:x\mapsto a+rx$ is a homeomorphism.
