Spaces for which all intermediate spaces are Wallman equivalent

AbstractA T1 space X is defined to be a WSM space provided that for any space Y between X and WX, any pair of disjoint closed subsets of Y have disjoint closures in WX. The WSM spaces have the property that all spaces between X and WX have equivalent Wallman compactifications. They are also the natural generalization (from T4 spaces to T1 spaces) of the concept of normality inducing spaces