In mathematics, a closure property refers to the property of a set being closed under some operation on its elements, which means that if you apply the operations to elements in the set, the result is also in the set.

Some examples:

the natural numbers
are closed under addition and multiplication, but not under subtraction or division
the regular languages
are closed under intersection, union, complementation, and pairwise concatenation (X.Y = {x.y | x in X, y in Y}), but not elementwise concatenation (2X = {x.x | x in X })
is closed under multiplication, but not under its converse, unless you are a creationist

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