Let X be a topological spaceMathworldPlanetmath. A development for X is a countableMathworldPlanetmath collectionMathworldPlanetmath F1,F2, of open coverings of X such that for any closed subset C of X and any point p in the complement of C, there exists a cover Fj such that no element of Fj which contains p intersects C. A space with a development is called developable.

A development F1,F2, such that FiFi+1 for all i is called a nested development. A theoremMathworldPlanetmath from Vickery states that every developable space in fact has a nested development.


  • 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
Title development
Canonical name Development
Date of creation 2013-03-22 14:49:49
Last modified on 2013-03-22 14:49:49
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Definition
Classification msc 54D20
Defines developable
Defines nested development
Defines Vickery’s theorem