Cantor set
Since the Cantor set is homeomorphic to the product formula_10, there is a continuous bijection formula_11 from the Cantor set onto formula_7. The composition formula_13 of formula_6 and formula_11 is a continuous function mapping the Cantor set onto the entire unit square. (Alternatively, we could use the theorem that every compact metric space is a continuous image of the Cantor set to get the function formula_13.)