Is there a mathematical notation to express the domain without the range or the range without the domain?

Question

According to the domain's Wikipedia page

I can express the domain and range of a function like this $$f:X\rightarrow Y$$

What if I am only interested in the domain of the function? Is it mathematically accepted to write this? $$f:X$$

What if I am only interested in the range?

I am asking if there is a mathematical notation to represent these concepts individually without presenting both at the same time.

Answer 1

One often sees $\operatorname{dom }f$ and $\operatorname{ran} f$ or $D(f)$ and $R(f)$ or $D_{f}$ and $R_{f}$ .

Of course, you can also say something like

When $f$ is a function, we will write “$\square f$” to mean the domain of $f$ and “$f\square$” to mean the codomain

or whatever. You're allowed to make up whatever notation you like, as long as you explain it clearly.