In an arbitrary topological space this may not be possible.

More precisely, a topological space has a certain kind of set, called open sets.

In all of the following definitions, X is again a topological space.

For another example consider the category of topological spaces, Top.

The open sets of a topological space, ordered by inclusion.

This makes a topological space that is no longer a manifold.

In many examples the are not just sets but rather topological spaces.

As the above section on topological spaces makes clear, analysis isn't just about continuity in the traditional sense of real numbers.

Some topological spaces may be endowed with a group law.

Let X be a topological space, and A a set.