Fσ set
Each closed set is an Fσ set. The set formula_2 of rationals is an Fσ set in formula_3. More generally, any countable set in a T1 space is an Fσ set, because every singleton formula_4 is closed. The set formula_5 of irrationals is not a Fσ set. In metrizable spaces, every open set is an Fσ set. The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set. The set formula_6 of all points formula_7 in the Cartesian plane such that formula_8 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:
formula_9
where formula_2, is the set of rational numbers, which is a countable set.
Examples
In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The complement of an Fσ set is a Gδ set.