KnowraEberlein–Šmulian theoremLinked fromLinked fromThe 3 pages that link to Eberlein–Šmulian theorem, each with the reason it gives.All 3Related 3Weak topologyRelated: It connects weak compactness to the behavior of sequences.Sequential compactnessRelated: It establishes a striking setting where a sequential condition fully captures compactness.Banach–Alaoglu theoremRelated: It highlights why compactness need not imply sequential compactness in the weak-* setting.