Linked from

The 15 pages that link to Arzelà–Ascoli theorem, each with the reason it gives.

• Uniform convergenceRelated: Uniform convergence is the function-space topology in which its compactness conclusions are formulated.

• Compact spaceRelated: It uses compactness to extract convergent subsequences of functions.

• Bolzano–Weierstrass theoremRelated: It extends subsequence extraction from finite-dimensional vectors to families of functions.

• Uniform continuityRelated: Equicontinuity extends the same uniform-control idea from one function to a family.

• Bounded setRelated: Uniform boundedness of function values is one condition in its compactness criterion.

• Compact operatorRelated: It supplies a standard test for compactness of operators whose outputs are functions.

• Normal familyNarrower topic: Normality is its locally uniform, spherical-metric counterpart for meromorphic functions.

• Peano existence theoremRelated: It supplies a convergent subsequence of approximations in a classical proof.

• Prokhorov's theoremCompared with: It is a parallel compactness criterion, but for function families rather than measures.

• Schauder fixed-point theoremRelated: It often verifies compactness when Schauder’s theorem is applied to function spaces.

• Stone–Weierstrass theoremCompared with: It concerns compactness of function families, not density of an algebra in all continuous functions.

• Heine–Cantor theoremRelated: It extends the theme of uniform control from one function to families of functions.

• Montel's theoremRelated: Cauchy estimates provide equicontinuity, allowing compactness arguments on compact subsets.

• Gromov's compactness theoremRelated: Both theorems obtain subsequential compactness from uniform control across a family.

• Kolmogorov continuity theoremCompared with: It concerns compactness of function families, while Kolmogorov’s criterion derives path regularity probabilistically.