# Closure of Irreducible Subspace is Irreducible

## Theorem

Let $X$ be a topological space.

Let $Y \subset X$ be an irreducible subspace.

Then its closure $\overline Y$ is also irreducible.

## Proof

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Let $X$ be a topological space.

Let $Y \subset X$ be an irreducible subspace.

Then its closure $\overline Y$ is also irreducible.

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