A set and a binary operator are said to exhibit closure if applying
the binary operator to two elements returns a value which is itself a member of .

The closure of a set
is the smallest closed set containing . Closed sets are closed under arbitrary
intersection, so it is also the intersection of all closed sets containing . Typically, it is just with all of its accumulation
points.

The term "closure" is also used to refer to a "closed" version of a given set. The closure of a set can be defined in several
equivalent ways, including

1. The set plus its limit points, also called "boundary" points, the union of which is also called the "frontier."

2. The unique smallest closed set containing the given
set.