On the class of continuous images of non-commutative Valdivia compacta

We investigate the class of continuous images of non-commutative Valdivia compact spaces, in particular its subclass of weakly non-commutative Corson countably compact spaces. A key tool is the study of non-commutative Corson countably compact spaces and their stability. The results are the non-commutative version of results by O. Kalenda (2003). Moreover, we present a study of retractional skeletons on Aleksandrov duplicates of ordinal spaces.