cofinite subset
Sign in to saveAlso known as set with finite complement, cofinite set
In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set. In other words, A contains all but finitely many elements of X. If the complement is not finite, but is countable, then one says the set is cocountable.
~4 min read
Article
9 sectionsContents
- Boolean algebras
- Cofinite topology
- Properties
- Double-pointed cofinite topology
- Other examples
- Product topology
- Direct sum
- See also
- References
In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set. In other words, A contains all but finitely many elements of X. If the complement is not finite, but is countable, then one says the set is cocountable.
These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the product topology or direct sum.
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