Name of this property : $x < y$ implies $f(x) < f(y)$

Question

For use in proving the independence of x for a functions rotation number. (think its because its Homeomorphic)

Answer 1

A function with the property $x < y \Rightarrow f(x) < f(y) $ can be called $\textbf{strictly monotone increasing}$.

Answer 2

I would call a function that obeys $x < y \to f(x) < f(y)$ for all $x,y$, a strictly increasing function.