PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (232)
Orphanage
Unclass'd
Unproven (519)
Corrections (23)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
[parent] strongly paracompact space (Definition)

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).



"strongly paracompact space" is owned by yark.
(view preamble | get metadata)

View style:

Other names:  strongly paracompact topological space
Also defines:  strongly paracompact, star-finite, star finite

This object's parent.
Log in to rate this entry.
(view current ratings)

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 1171 times total.

Classification:
AMS MSC: 54D20 (General topology :: Fairly general properties :: Noncompact covering properties )
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)