# nLab saturated set

## Definition

A subset $S$ of a topological space $X$ is called saturated if it is the intersection of its open neighborhoods.

## Properties

• If $X$ is T1, every subset of $X$ is saturated. In particular, every singleton subset of a T1 space is the intersection of its open neighborhoods.

• $X$ is not T1 precisely if there exists a non-saturated singleton.