Definition:F-Sigma Set
Jump to navigation
Jump to search
Definition
Let $T = \struct {S, \tau}$ 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
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): sigma: 2.
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 15$