As for the linear case, compactness for the strong topology is very restrictive. 聽Since the beginning of聽the fixed point theory, weak-compactness offered an acceptable alternative in Banach spaces. But when we deal with metric spaces, this natural extension is no longer easy to implement. One has to go back to the linear case and investigate the weak-topology with a new eye. 聽In this talk, I will share some of the ideas of how to extend concepts of linear nature to nonlinear spaces, i.e., metric spaces.
