Point is Contained in Irreducible Component

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Theorem

Let $X$ be a topological space.

Let $x\in X$ be a point.


Then $x$ is contained in some irreducible component of $X$.


Proof

Because Trivial Topological Space is Irreducible, this is a special case of Irreducible Subspace is Contained in Irreducible Component.

$\blacksquare$