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.
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- Vickery, C.W. (1940). "Axioms for Moore spaces and metric spaces". Bull. Amer. Math. Soc. 46: 560–564. doi:10.1090/S0002-9904-1940-07260-X. JFM 66.0208.03. Zbl 0061.39807.