##  [Stone Representation Theorem](/index.php/stone-representation-theorem) 

  ##  [Stone Representation Theorem](https://mathlogic.quantumdictionary.io/stone-representation-theorem-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem stating that every Boolean algebra is isomorphic to an algebra of sets: concretely, it is isomorphic to the algebra of clopen (simultaneously closed and open) subsets of a compact, totally disconnected Hausdorff topological space (the Stone space of the algebra).

 

 

 

 

 





 

 



 ##  [Stone Representation Theorem](https://puremath.quantumdictionary.io/stone-representation-theorem-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem establishing a dual equivalence between the category of Boolean algebras and the category of zero-dimensional compact Hausdorff spaces (Stone spaces) by representing each Boolean algebra as the algebra of clopen subsets of a canonical compact space of ultrafilters.