<P> These three properties define an abstract closure operator . Typically, an abstract closure acts on the class of all subsets of a set . </P> <P> If X is contained in a set closed under the operation then every subset of X has a closure . </P> <Ul> <Li> 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 . </Li> <Li> 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 . </Li> <Li> In matroid theory, the closure of X is the largest superset of X that has the same rank as X . </Li> <Li> In set theory, the transitive closure of a set . </Li> <Li> In set theory, the transitive closure of a binary relation . </Li> <Li> In algebra, the algebraic closure of a field . </Li> <Li> In commutative algebra, closure operations for ideals, as integral closure and tight closure . </Li> <Li> In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset . </Li> <Li> In 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 . </Li> <Li> In group theory, the conjugate closure or normal closure of a set of group elements is the smallest normal subgroup containing the set . </Li> <Li> In mathematical analysis and in probability theory, the closure of a collection of subsets of X under countably many set operations is called the σ - algebra generated by the collection . </Li> </Ul> <Li> 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 . </Li>

Which operations is the set of even numbers closed under