I am looking at space filling curves. Essentially their is a mapping $f: I \to \mathcal{Q}$ where I is an interval in $\mathbb{R}$ such as $[0,1]$ and $\mathcal{Q}$ is a square $[0,1]^2$.
For the mapping $f$ to define a space filling curve it has to be continuous, surjective and we have to show every $t \in I$ is uniquely mapped to a point $f(t) \in \mathcal{Q}$
What does it mean to say uniquely mapped?
I thought it meant every point in the pre image had a unique point in the image. But this would make the mapping injective but a space filling curve can not be injective.