Normality inducing spaces

AbstractIt is known that every continuous function with T1 domain and T4 range has a unique Wallman extension and that every nonnormal T3 space is the range of a continuous function which is not Wallman extendible. In this paper we introduce the concept of a normality inducing space and show that if X is a T4 space, then every continuous function with domain X and T3 range is Wallman extendible if and only if X is a normality inducing space. Further if X is a normality inducing space, Y a T3 space and f : X → Y is continuous then cly(f[X] is normal