Q:

Existence of continuous surjection from open unit square to closed unit square

Does there exists a continuous surjection from (0,1)×(0,1) to [0,1]×[0,1]?  
I have found such a function from (0,1) to [0,1].  I just want to generalize it. 

A:

If $f: (0,1) \to [0,1]$ is a continuous surjection, then $F(x,y)=(f(x), f(y))$ is also continuous and onto from $(0,1)^2$ to $[0,1]^2$.

