High Quality Content by WIKIPEDIA articles! In mathematics, the Wallman compactification is a compactification of T1 topological spaces that was constructed by Wallman (1938). THe points of the Wallman compactification X of a space X are the maximal families of closed nonempty subsets of X such that is closed under finite intersections. A Base for the closed sets is given by the families F containing a fixed closed set F of X. FOr normal spaces, the Wallman compactification is essentially the same as the Stone ech compactification.