F-sigma set

From Free net encyclopedia

In mathematics, an F_σ 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:union).

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

The complement of a F_σ set is a G_δ set. In a metrizable space, any closed set is a G_δ 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.

Template:Topology-stubpl:Zbiór typu F-sigma