Definition:G-Delta Set
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
A $G_\delta$ set ($G$-delta set) is a set which can be written as a countable intersection of open sets of $T$.
Also see
- $F_\sigma$ ($F$-Sigma) Set
- Complement of $F_\sigma$ Set is $G_\delta$ Set
- Complement of $G_\delta$ Set is $F_\sigma$ Set
- Results about $G_\delta$ sets can be found here.
Linguistic Note
The name $G_\delta$ originates from the German:
- G for Gebiet, which is German for area or neighborhood (used in the sense open set in this case)
- $\delta$ (Greek d) for Durchschnitt, which is German for set intersection.
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
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 15$