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strongly paracompact space
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(Definition)
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A collection $\mathcal{A}$ of sets is said to be star-finite if each member of $\mathcal{A}$ meets only finitely many members of $\mathcal{A}$
A topological space $X$ is said to be strongly paracompact if every open cover of $X$ has a star-finite open refinement.
A star-finite open cover of a topological space is clearly locally finite. Therefore, every strongly paracompact space is paracompact (as the name suggests).
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"strongly paracompact space" is owned by yark.
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(view preamble | get metadata)
| Other names: |
strongly paracompact topological space |
| Also defines: |
strongly paracompact, star-finite, star finite |
This object's parent.
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Cross-references: paracompact, locally finite, open refinement, open cover, topological space, collection
There is 1 reference to this entry.
This is version 2 of strongly paracompact space, born on 2007-05-24, modified 2007-05-24.
Object id is 9459, canonical name is StronglyParacompact.
Accessed 2127 times total.
Classification:
| AMS MSC: | 54D20 (General topology :: Fairly general properties :: Noncompact covering properties ) |
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Pending Errata and Addenda
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