development
Let X be a topological space. A development for X is a countable
collection
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 Fi⊂Fi+1 for all i is called a nested development. A theorem from Vickery states that every developable space in fact has a nested development.
References
- 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 |