strongly paracompact space
A collection
𝒜 of sets is said to be star-finite
if each member of 𝒜
meets only finitely many members of 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).
| Title | strongly paracompact space |
|---|---|
| Canonical name | StronglyParacompactSpace |
| Date of creation | 2013-03-22 17:09:01 |
| Last modified on | 2013-03-22 17:09:01 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 5 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 54D20 |
| Synonym | strongly paracompact topological space |
| Defines | strongly paracompact |
| Defines | star-finite |
| Defines | star finite |