In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms.
be a topological space.
is a countable collection
of open coverings of
, such that for any closed subset
, there exists a cover
such that no element of
A space with a development is called developable.
is called a nested development.
A theorem from Vickery states that every developable space in fact has a nested development.
, 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.