Terminology: Contraction *of* normed spaces? *Between* normed spaces? *On* normed spaces?

Question

I have a terminological question. Suppose $X$ and $Y$ are normed spaces, and let $f$ be a contraction $X \to Y$. Which of the following expressions is correct?

1. $f$ is a contraction of normed spaces.
2. $f$ is a contraction between normed spaces.
3. $f$ is a contraction on normed spaces.
4. $f$ is a normed space contraction.
5. Something else suggested by you.

I need an expression in these lines as I would like to differentiate, even from the linguistic point of view, a contraction acting from a normed space to another normed space from a contraction acting from a normed ring to another normed ring.