Assess graduate students' ability to recall and state accurately the hypotheses and conclusions of the Arzelà–Ascoli, Banach–Alaoglu, and Rellich–Kondrachov compactness theorems; specify the ambient spaces and topologies involved (e.g., C(K) with the sup norm, dual ball with the weak* topology, Sobolev spaces and Lp embeddings), list key hypotheses (equicontinuity, boundedness, embedding/regularity conditions), and identify standard corollaries—no proofs required.