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.
$\blacksquare$