##  [Stone Space](/stone-space) 

  ##  [Stone Space](https://mathlogic.quantumdictionary.io/stone-space-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A Stone space is a compact, Hausdorff, totally disconnected topological space that arises as the space of ultrafilters of a Boolean algebra or, in model theory, as the space of complete n-types (type space) equipped with the topology generated by sets of types containing a given formula; points correspond to ultrafilters/complete types and clopen sets correspond to syntactic Boolean combinations o

 

 

 

 

 





 

 



 ##  [Stone Space](https://puremath.quantumdictionary.io/stone-space-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A compact, Hausdorff, zero-dimensional (totally disconnected) topological space that arises as the dual object of a Boolean algebra under Stone duality; points correspond to ultrafilters and clopen sets correspond to algebra elements.