Arzelà–Ascoli Theorem
Uniform boundedness and equicontinuity provide convergent subsequences in spaces of continuous functions on compact domains. Compare this criterion with mere pointwise boundedness to see what controls convergence uniformly.
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Continuous Function · Uniform Convergence · Topological Compactness
Where to read
Start here: Notes on Partial Differential Equations
John K. Hunter · Lecture notes · English · Free full text
§1.5 Compactness, Theorem 1.14, printed p. 6
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Real Analysis in the library · Preparation and skip guidance