ideaalsetest
Ideaalsetest is a term used in Estonian mathematical literature to refer to the collection of subsets of a given set that form an ideal. An ideaalset (plural ideaalset) on a base set X is a nonempty family I of subsets of X that satisfies two key properties: downward closure (if A is in I and B is a subset of A, then B is also in I) and closure under finite unions (if A and B are in I, then A ∪ B is in I). In many treatments, an ideal must not contain the whole set X.
Common examples illustrate the concept. The finite-sets ideal Fin(X) consists of all finite subsets of an infinite
Relation to other concepts is important. The dual notion to an ideal is a filter, which is
See also: ideal (set theory), σ-ideal, filter, Boolean algebra.