Definition:G-Delta Set
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Definition
Let $\left({X, \tau}\right)$ 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 $X$.
Linguistic Note
The name $G_\delta$ originates from the German:
- G for Gebiet, which is German for area or neighborhood (here used in the sense open set in this case)
- $\delta$ (Greek d) for Durchschnitt, which is German for intersection.
Also see
- $F_\sigma$ (F-Sigma) Set
- Complement of F-Sigma Set is G-Delta Set
- Results about $G_\delta$ sets can be found here.
Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$
- René L. Schilling: Measures, Integrals and Martingales (2005)... (previous)... (next): $\S 15$