Definition:Generic Point of Topological Space

Definition

Let $T = \struct {S, \tau}$ 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 $\set x$ 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 $T$.

Also see

• Equivalence of Definitions of Generic Point of Topological Space

• Results about generic points of topological spaces can be found here.