In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms.

Let be a countable collection of open dense subsets.

The algebraic K3 surfaces form a countable collection of 19-dimensional subvarieties of it.

For a countable collection of formulas of degree 1, we may define as above; then define to be the closure of .

Note that any σ-algebra generated by a countable collection of sets is countable, but the converse need not hold.

The union of a countable collection of polar sets is polar.

A countable collection of sets is necessarily countably locally discrete.

A set that contains the intersection of a countable collection of dense open sets is called comeagre or residual.

It states that any countable collection of non-empty sets must have a choice function.

AC is particularly useful for the development of analysis, where many results depend on having a choice function for a countable collection of sets of real numbers.