Complex sentence: Peano's curve is dense in the unit square, and was used by Peano to construct a continuous function from the unit interval to the unit square, motivated by an earlier result of Georg Cantor that these two sets have the same cardinality.
Split into simpler sentences: Peano's curve is a continuous function from the unit interval onto the unit square. Peano was motivated by an earlier result of Georg Cantor that these two sets have the same cardinality.