Page "Space-filling curve" Paragraph 17

Finally, one can extend to a continuous function whose domain is the entire unit interval.

This can be done either by using the Tietze extension theorem on each of the components of, or by simply extending " linearly " ( that is, on each of the deleted open interval in the construction of the Cantor set, we define the extension part of on to be the line segment within the unit square joining the values and ).