Development (topology)
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 topological space. A development for is a countable collection of open coverings of, such that for any closed subset and any point in the complement of, there exists a cover such that no element of which contains intersects. A space with a development is called developable.
A development such that for all is called a nested development. A theorem from Vickery states that every developable space in fact has a nested development. If is a refinement of, for all, then the development is called a refined development.
Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable.
