Weak-* topology on dual X*; Banach-Alaoglu: closed-unit-ball of X* is weak-*-compact. Foundation of variational + optimisation methods. Mazur's theorem: weak vs norm closure for convex.
Weak-* topology on dual X*; Banach-Alaoglu: closed-unit-ball of X* is weak-*-compact. Foundation of variational + optimisation methods. Mazur's theorem: weak vs norm closure for convex.