this is a problem from kenneth ross's book "elementary analysis: the theory of calculus" in section 21 (metric spaces):

we say a function f maps a set E onto a set F provided f(E)=F.

1. show that there is a continuous function mapping the unit square {(x_1,x_2) in R^2: 0<=x_1<=1, 0<=x_2<=1} onto [0,1].

2. do you think there is a continuous function mapping [0,1] onto the unit square?