Development (topology)

From Wikipedia, the free encyclopedia

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.

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.

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

References

Retrieved from "https://en.wikipedia.org/w/index.php?title=Development_(topology)&oldid=711460912"
This content was retrieved from Wikipedia : http://en.wikipedia.org/wiki/Development_(topology)
This page is based on the copyrighted Wikipedia article "Development (topology)"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA