Examples
- In topology and related branches, the relevant operation is taking limits. The topological closure of a set is the corresponding closure operator. The Kuratowski closure axioms characterize this operator.
- In linear algebra, the linear span of a set X of vectors is the closure of that set; it is the smallest subset of the vector space that includes X and is closed under the operation of linear combination. This subset is a subspace.
- In matroid theory, the closure of X is the largest superset of X that has the same rank as X.
- In set theory, the transitive closure of a set.
- In set theory, the transitive closure of a binary relation.
- In algebra, the algebraic closure of a field.
- In commutative algebra, closure operations for ideals, as integral closure and tight closure.
- In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset.
- In the theory of formal languages, the Kleene closure of a language can be described as the set of strings that can be made by concatenating zero or more strings from that language.
- In group theory, the conjugate closure or normal closure of a set of group elements is the smallest normal subgroup containing the set.
Read more about this topic: Closure (mathematics)
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