In mathematics, the Wallman compactification, generally called WallmanâÂÂShanin compactification is a compactification of T<sub>1</sub> topological spaces that was constructed by .
The points of the Wallman compactification ÃÂX of a space X are the maximal proper filters in the poset of closed subsets of X. Explicitly, a point of ÃÂX is a family of closed nonempty subsets of X such that is closed under finite intersections, and is maximal among those families that have these properties. For every closed subset F of X, the class æ<sub>F</sub> of points of ÃÂX containing F is closed in ÃÂX. The topology of ÃÂX is generated by these closed classes.
For normal spaces, the Wallman compactification is essentially the same as the StoneâÂÂÃÂech compactification.