Y-Coordinate of a Point - Notation

Question

Given point $P$ on curve $\omega$, what expression is generally use to denote the $y$-coordinate of point $P$, also, the $x$-coordinate. Would it be $P_y$? Also, let $\omega$ be in $\mathbb{R}^2$, not in $\mathbb{C}$, so it cannot be $\text{Im}(P)$

Answer 1

I think notation varies depending on who is writing and for what purpose, but I think the two options I see most often are

1. Write the coordinates of $P$ as $(P_x, P_y)$, or
2. Introduce projection functions $x$ and $y: \mathbb{R}^2 \rightarrow \mathbb{R}$, so that the x-coordinate is $x(P)$ and the y-coordinate is $y(P)$.