This open set can then be used to distinguish between the two points.

That is, all of the points not belonging to a certain open sets forms a closed set.

Let be an open set in the complex plane.

It can be constructed by taking the union of all the open sets contained in A.

Three levels up, an open set of doors faced the landing.

The theory has been generalized to more general open sets, too.

We shall show that the complement of S is an open set.

Note that the neighbourhood need not be an open set itself.

It is in general not true that every open set is also closed.

Every open set is a union of a collection of these.