In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for fermé (French: closed) and σ for somme (French: sum, union).
In metrizable spaces, every open set is an Fσ set. The complement of an Fσ set is a Gδ set. In a metrizable space, any closed set is a Gδ set.
The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set.
Examples
Each closed set is an Fσ set.
The set 
of rationals is an Fσ set. The set 
of irrationals is not a Fσ set.
Each enumerable set is an Fσ set, because a point x is closed.
For example, the set A of all points (x,y) 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 , is the set of rational numbers, which is a countable set.
See also
- Gδ set — the dual notion.
- Borel hierarchy
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