A note on absolute approximate retracts

The notion of an absolute approximate retract for a class Q of topological spaces (or an AAR(Q)-space) generalizes the concept of an absolute retract for the class Q. For many classes Q, it is shown that AAR(Q)-spaces are preserved under retraction mappings and that a fully normal AAR(Q)-space X must be contractible and can be expressed as a product of finite-dimensional compacta if and only if X is homeomorphic to a cube or is a finite-dimensional AR-space.