What is "cofiniteness"

In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set. In other words, A contains all but finitely many elements of X. If the complement is not finite, but it is countable, then one says the set is cocountable.

These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the product topology or direct sum.