|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In mathematics, the '''Wallman compactification''' is a [[compactification (mathematics)|compactification]] of [[T1 space|T<sub>1</sub> topological spaces]] that was constructed by {{harvtxt|Wallman|1938}}.
| | Hello, I'm Dominique, a 30 year old from Vaulx-Lez-Chimay, Belgium.<br>My hobbies include (but are not limited to) Book collecting, Trainspotting and watching The Vampire Diaries.<br><br>Feel free to visit my page; [http://nitishdeoli.com/blogs/post/20702 wordpress dropbox backup] |
| | |
| The points of the Wallman compactification ω''X'' of a space ''X'' are the maximal proper [[filter (mathematics)|filter]]s in the [[poset]] of closed subsets of ''X''. Explicitly, a point of ω''X'' is a family <math>\mathcal F</math> of closed nonempty subsets of ''X'' such that <math>\mathcal F</math> is closed under finite intersections, and is maximal among those families that have these properties. For every closed subset ''F'' of ''X'', the class Φ<sub>''F''</sub> of points of ω''X'' containing ''F'' is closed in ω''X''. The topology of ω''X'' is generated by these closed classes.
| |
| | |
| For [[normal space]]s, the Wallman compactification is essentially the same as the [[Stone–Čech compactification]].
| |
| | |
| == See also ==
| |
| * [[Lattice (order)]]
| |
| * [[Pointless topology]]
| |
| | |
| ==References==
| |
| *{{springer|id=Wallman_compactification|first=P.S. |last=Aleksandrov}}
| |
| *{{citation|first=Henry |last=Wallman|authorlink=Henry Wallman|title=Lattices and topological spaces |volume= 39 |year=1938|pages= 112–126
| |
| |url=http://links.jstor.org/sici?sici=0003-486X%28193801%292%3A39%3A1%3C112%3ALATS%3E2.0.CO%3B2-U }}
| |
| | |
| [[Category:General topology]]
| |
| [[Category:Compactification]]
| |
| | |
| | |
| {{topology-stub}}
| |
Latest revision as of 05:49, 1 June 2014
Hello, I'm Dominique, a 30 year old from Vaulx-Lez-Chimay, Belgium.
My hobbies include (but are not limited to) Book collecting, Trainspotting and watching The Vampire Diaries.
Feel free to visit my page; wordpress dropbox backup