Definition:G-Delta Set

Definition

Let $\left({X, \vartheta}\right)$ 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): $\S 15$