Closure (mathematics)

Definition

In mathematics, a subset of a larger set is closed under a given operation on the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are.

Related concepts

Algebra of sets Algebraic closure Algebraic set Algebraic structure Associative operation Axioms Binary operation Binary relation Ceiling function Closed set Closure (computer science)Closure (topology)Closure operator Commutative ring Conjugate closure Convex hull Convex set Countable Cyclic group Equivalence relation Eric W. Weisstein Existential quantifier Field (algebra)Field (mathematics)Formal language Function (mathematics)Garrett Birkhoff Generating set Geometry Greatest-lower-bound property Group (mathematics)Group theory Ideal (ring theory)Idempotent Identity (mathematics)Identity element If and only if Infix notation Integral closure Integral domain Inverse element Kleene closure Kuratowski closure axioms Limit of a sequence Linear algebra Linear combination Linear span Magma (algebra)MathWorld Mathematical analysis Matroid Monotonic Multivariate function Natural number Normal subgroup Nullary Operation (mathematics)Ordered pair Partial function Partial operation Partially ordered set Polynomial Preorder Principal ideal Probability theory Radical of an ideal Reflexive closure Reflexive relation Roots of a polynomial Scalar multiplication Set (mathematics)Set inclusion Set intersection Sigma-algebra Span (linear algebra)Subgroup Subset Substructure (mathematics)Symmetric closure Symmetric relation Topological closure Topological space Transitive closure Transitive relation Transitive set Unary operation Universally quantified Vector space Zariski-closed Zariski closure

14 concepts already in your glossary