An F set is a countable union of closed sets.

For example, the three dimensional Euclidean space is not a countable union of its affine planes.

An open set on the real line has the characteristic property that it is a countable union of disjoint open intervals.

More generally, any countable union of null sets is null.

Any finite or countable union of shy sets is also shy.

Strongly Lindelöf spaces are closed under taking countable unions, subspaces, and continuous images.

Every open set in the subshift of finite type is a countable union of cylinder sets.

That is, the Borel sets are closed under countable unions.

Then every open subset of the real line is a countable union of open intervals.

In G spaces, every open set is the countable union of closed sets.