The space X is a quotient space or identification space.

One can form the quotient of a pointed space X under any equivalence relation.

The classical definition of a sheaf begins with a topological space 'X'.

One may talk about balls in any topological space X, not necessarily induced by a metric.

The cone on a space X is always contractible.

A cover of a topological space X is open if all its members are open sets.

When the space X is said to be a Lindelöf space.

There are various ways in which two subsets of a topological space X can be considered to be separated.

A topological space X is connected if these are the only two possibilities.

We have the following inequalities, for a metric space X: