Noncommutative Valdivia compacta

Abstract

We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space K, we show that K is Corson if and only if every continuous image of K has a retractional skeleton.

Cited by in corpus (6)

• Monotone retractability and retractional skeletons
• Families of retractions and families of closed subsets on compact spaces
• Families of continuous retractions and function spaces
• Characterizing Corson and Valdivia compact spaces
• $r$-skeletons on the Alexandroff duplicate
• On the class of continuous images of non-commutative Valdivia compacta