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About: Development (topology)     Goto   Sponge   NotDistinct   Permalink

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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. Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable.