Definition:Generic Point of Topological Space

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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 $T$.


Also see