##  [Baire Category Method](/baire-category-method) 

  ##  [Baire Category Method](https://mathlogic.quantumdictionary.io/baire-category-method-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 technique that exploits the Baire category theorem to establish existence or genericity statements by showing that the set of objects with a desired property is comeagre (a countable intersection of dense open sets) or at least nonmeagre in a Baire space such as a complete metric space or a locally compact Hausdorff space.

 

 

 

 

 





 

 



 ##  [Baire Category Method](https://puremath.quantumdictionary.io/baire-category-method-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 technique that applies the Baire category theorem to obtain generic existence or density results by showing that a countable intersection of dense open sets (a dense G_δ set) contains the typical objects with a given property in a complete metric or Baire space.