Development of a topological space

This article or section of article is sourced from:Planetmath

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.