Stone space | Wikipedia audio article
Channel: wikipedia tts
Date: 28/03/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Stone_space





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SUMMARY
=======
In topology, and related areas of mathematics, a Stone space is a non-empty compact totally disconnected Hausdorff space. Such spaces are also called profinite spaces. They are named after Marshall Harvey Stone.
A form of Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the Boolean algebra of clopen sets of a Stone space.  This isomorphism forms a category-theoretic duality between the categories of Boolean algebras and Stone spaces.
Equivalently, Stone space is a topological space such that:

Compact, totally separated;
Compact, 
  
    
      
        
          T
          
            0
          
        
      
    
    {\displaystyle T_{0}}
  , zero-dimensional;
Coherent and Hausdorff.