These things, which can never be di erentiable, include one named for Osgood which is non-self-intersecting and one named for Gosper which is also known as the     owsnake  and covers the Gosper island.
The Hahn-Mazurkiewicz theorem states that these things can only exist in spaces ful lling certain criteria. These things, which can never be di erentiable, include one named for Osgood which is non-self-intersecting and one named for Gosper which is also known as the     owsnake  and covers the Gosper island. One of these things was constructed in order to create a surjective mapping from the unit interval to the unit square; that one is named for Peano, while another one with the same property is named for Hilbert. For ten points, identify this class of plane curves which completely cover a given multidimensional area.
The Hahn-Mazurkiewicz theorem states that these things can only exist in spaces ful lling certain criteria.
space-filling curves [accept Peano curves until  Peano  is read, accept plane- lling curves]