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# Fσ set

In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for ' ("French": closed) and σ for ' ("French": sum, union).

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

The complement of an F&sigma; set is a G&delta; set. In a metrizable space, any closed set is a Gδ set.

The union of countably many F&sigma; sets is an F&sigma; set, and the intersection of finitely many Fσ sets is an Fσ set.

For example, the set $A$ of all points $\left(x,y\right)$ in the Cartesian plane such that $x/y$ is rational is an Fσ set because it can be expressed as the union of all the lines passing through the origin with rational slope:

:

where $mathbb\left\{Q\right\}$, is the set of rational numbers, which is a countable set.

ee also

*Gδ set — the dual notion.
*Borel hierarchy

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