Wallman compactification

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

The points of the Wallman compactification ωX 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.

See also

• Lattice
• Pointless topology

References

• Aleksandrov, P.S. (2001), "Wallman compactification", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=w/w097050 
• Wallman, Henry (1938), Lattices and topological spaces, 39, pp. 112–126, http://links.jstor.org/sici?sici=0003-486X%28193801%292%3A39%3A1%3C112%3ALATS%3E2.0.CO%3B2-U