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Homedevelopment

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# development

Let $X$ be a topological space. A *development* for $X$ is a countable collection $F_{1},F_{2},\ldots$ 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 $F_{j}$ such that no element of $F_{j}$ which contains $p$ intersects $C$. A space with a development is called *developable*.

A development $F_{1},F_{2},\ldots$ such that $F_{i}\subset F_{{i+1}}$ 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.

Defines:

developable, nested development, Vickery's theorem

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

54D20*no label found*

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