On Valdivia Christmas (compact) trees and their consequences in Banach spaces

General topology plays an important role in the study of Banach spaces. In this talk, after giving a glance to the main relations between general topology and Banach spaces, the classes of Corson, Valdivia and non-commutative Valdivia compact spaces, will be presented. Special care will be given to the class of set-theoretical compact trees. This class will be used to address open questions in this field.