# Stone's Representation Theorem for Boolean Algebras

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## Theorem

Let $B$ be a Boolean algebra.

Let $S$ be the Stone space of $B$.

Then:

- The set of clopen sets in $S$ is a Boolean algebra under union, intersection, and complementation in $S$.
- That Boolean algebra is isomorphic to $B$.

## Proof

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## Source of Name

This entry was named for Marshall Harvey Stone.