# Definition:F-Sigma Set

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## Contents

## Definition

Let $T = \left({S, \tau}\right)$ 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 $T$.

## Also see

- Definition:$G_\delta$ (G-Delta) Set
- Complement of $F_\sigma$ Set is $G_\delta$ Set
- Complement of $G_\delta$ Set is $F_\sigma$ Set

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

## 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**set union**.

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{I}: \ \S 1$ - 2005: René L. Schilling:
*Measures, Integrals and Martingales*... (previous) ... (next): $\S 15$