Definition, Meaning & Synonyms
baire
noun
/ˈbeər/
Definition
Baire refers to a topological space that satisfies the Baire category theorem, which states that in a complete metric space, the intersection of countably many dense open sets is dense.
Examples
- The Baire category theorem plays a critical role in functional analysis.
- In the context of Baire spaces, the intersection pattern of dense subsets provides insights into continuity.
- Many results in topology stem from applications of the Baire category principles.
Meaning
In mathematics, particularly in topology, Baire pertains to concepts that deal with the properties of topological spaces related to completeness and density.
Synonyms
- Category space
- Dense space
- Topological space
