A note on Wallman extendible functions

Abstract

It is known that any continuous function into a T 4 {T_4} space has a unique continuous Wallman extension, and that any continuous Wallman extension of a continuous function with a T 3 {T_3} range must be unique. We show that for any T 3 {T_3} space Y Y which is not T 4 {T_4} there exists a T 3 {T_3} space X X and a continuous function f : X → Y f:X \to Y which has no continuous Wallman extension.