Definition:F-Sigma Set

Definition

Let $T = \left({S, \vartheta}\right)$ be a topological space.

An $F_\sigma$ set (F-Sigma set) is a set which can be written as a countable union of closed sets of $T$.

Linguistic Note

The name $F_\sigma$ originates from the French:

• F for Fermé, which is French for closed
• $\sigma$ (Greek s) for somme, which is French for union.

Also see

• $G_\delta$ (G-Delta) Set
• Complement of F-Sigma Set is G-Delta Set

• Results about $F_\sigma$ sets can be found here.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$