x_n ⇀ x iff φ(x_n) → φ(x) for all φ ∈ X*. Bounded sets weakly pre-compact (reflexive X); Banach-Alaoglu: B_{X*} weak-* compact.
x_n ⇀ x iff φ(x_n) → φ(x) for all φ ∈ X*. Bounded sets weakly pre-compact (reflexive X); Banach-Alaoglu: B_{X*} weak-* compact.