In mathematics, an F_σ set (pronounced F-sigma set) is a countable union of closed sets. The notation originated in French with F for fermé (French: closed) and σ for somme (French: sum, union).

The complement of an F_σ set is a G_δ set.

F_σ is the same as ${\displaystyle \mathbf {\Sigma } _{2}^{0}}$ in the Borel hierarchy.

Each closed set is an F_σ set.

The set ${\displaystyle \mathbb {Q} }$ of rationals is an F_σ set in ${\displaystyle \mathbb {R} }$. More generally, any countable set in a T₁ space is an F_σ set, because every singleton ${\displaystyle \{x\}}$ is closed.

The set ${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$ of irrationals is not an F_σ set.

In metrizable spaces, every open set is an F_σ set.

The union of countably many F_σ sets is an F_σ set, and the intersection of finitely many F_σ sets is an F_σ set.