A subset of a topological space is called a $F_\sigma$ set if it equals the union of a countable collection of closed sets.

The complement of a $F_\sigma$ set is a $G_\delta$ set.

For instance, the $X$ set of all points $(x,y)$ in the plane such that either $y = 0$ or $x/y$ is rational is an $F_\sigma$ set because it can be expressed as the union of a countable set of lines: $$X = \{(x,0) \mid x \in \mathbb{R} \} \cup \bigcup_{r \in \mathbb{Q}} \{(ry,y) \mid y \in \mathbb{R}\}$$