# Definition:Generic Point of Topological Space

## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $x \in S$ be an element of $S$.

### Definition 1

The point $x$ is a generic point of $T$ if and only if the closure of the singleton $\left\{{x}\right\}$ is $S$.

### Definition 2

The point $x$ is a generic point of $T$ if and only if $x$ is contained in every non-empty open subset of $T$.