In mathematics, an F<sub>ÃÂ</sub> set (pronounced F-sigma set) is a countable union of closed sets. The notation originated in French with F for (French: closed) and ÃÂ for (French: sum, union).
The complement of an F<sub>ÃÂ</sub> set is a G<sub>δ</sub> set.
F<sub>ÃÂ</sub> is the same as in the Borel hierarchy.
Each closed set is an F<sub>ÃÂ</sub> set.
The set of rationals is an F<sub>ÃÂ</sub> set in . More generally, any countable set in a T<sub>1</sub> space is an F<sub>ÃÂ</sub> set, because every singleton is closed.
The set of irrationals is not an F<sub>ÃÂ</sub> set.
In metrizable spaces, every open set is an F<sub>ÃÂ</sub> set.
The intersection or union of finitely many F<sub>ÃÂ</sub> sets is an F<sub>ÃÂ</sub> set.
Assuming the Axiom of countable choice, the union of countably many F<sub>ÃÂ</sub> sets is an F<sub>ÃÂ</sub> set.
The set of all points in the Cartesian plane such that is rational is an F<sub>ÃÂ</sub> 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.