Wallman compactification

Wallman compactification

In mathematics, the Wallman compactification is a compactification of T1 topological spaces that was constructed by harvtxt|Wallman|1938.

The points of the Wallman compactification ω"X" of a space "X" are the maximal families Φ of closed nonempty subsets of "X" such that Φ is closed under finite intersections. A base for the closed sets is given by the families Φ"F" containing a fixed closed set "F" of "X".

For normal spaces, the Wallman compactification is essentially the same as the Stone–Čech compactification.

References

*springer|id=w/w097050|first=P.S. |last=Aleksandrov
*citation|first=Henry |last=Wallman|authorlink=Henry Wallman|title=Lattices and topological spaces|volume= Ann of Math. |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


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