functions - Bijection from $[0,1]^3$ to $[0,1]$?

Is there any bijection from $[0,1]^3$ to $[0,1]$? How can I construct it?

Answer

Hint:

If there exists a surjection between $A$ to $B$ and a surjection between $B$ to $A$, then there exists a bijection between $A$ to $B$. In your case, space filling curves are surjections from $[0,1]$ to $[0,1]^3$. It should be easy to find a surjection going the other way.