Development of a topological space

Definition
Let $$X$$ be a topological space. A development for $$X$$ is a countable collection $$F_1, F_2, \ldots$$ of open covers of $$X$$, such that for any closed subset $$C \subset X$$ and any point $$p \notin C$$, there exists a $$F_j$$ such that no member of $$F_j$$ which contains $$p$$ intersects $$C$$.

A topological space which has a development is termed a developable space.