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The 53 pages that link to Uniform convergence, each with the reason it gives.

• Augustin-Louis CauchyBroader topic: Cauchy’s early treatment of function series raised questions later clarified by uniform convergence.

• Power seriesNarrower topic: Uniform convergence helps justify exchanging limits with operations on power series.

• Real analysisCompared with: Unlike pointwise convergence, it preserves continuity under standard conditions.

• Pointwise convergenceCompared with: Unlike pointwise convergence, it controls approximation uniformly over the entire domain.

• SupremumRelated: Its error bound is expressed as a supremum over all domain points.

• Absolute convergenceRelated: Uniform convergence is distinct from absolute convergence, despite both strengthening ordinary convergence.

• Cauchy criterionRelated: Uniform Cauchy criteria test function sequences by pairwise differences across all inputs.

• Banach fixed-point theoremRelated: Function-space versions often use a supremum metric and completeness under uniform convergence.

• Laurent seriesRelated: Uniform convergence on compact subannuli justifies termwise differentiation and integration.

• Radius of convergenceCompared with: Pointwise convergence throughout the disk does not by itself establish uniform convergence on the whole disk.

• Almost sure convergenceCompared with: Almost sure convergence allows pointwise rates to vary across outcomes.

• Karl WeierstrassRelated: Uniform convergence supplies key conditions for passing limits through function operations.

• Arzelà–Ascoli theoremRelated: The theorem guarantees subsequences converging in this topology, not merely pointwise.

• Convergence in distributionCompared with: Convergence in distribution does not generally require uniform convergence of distribution functions.

• Dominated convergence theoremCompared with: Uniform convergence can exchange limits and integrals on finite-measure spaces through a different control.

• Lebesgue differentiation theoremCompared with: Differentiation holds almost everywhere, not uniformly over all points.

• Dirichlet seriesRelated: Uniform convergence on suitable regions justifies analytic operations on the series.

• Supremum normRelated: Convergence in the supremum norm is precisely uniform convergence when the norm is finite.

• Uniform continuityRelated: Uniform limits of uniformly continuous functions remain uniformly continuous.

• Almost-everywhere convergenceCompared with: Almost-everywhere convergence permits exceptional points and offers no uniform error bound.

• Rational approximationRelated: Uniform convergence describes approximation quality over an entire domain, not just pointwise.

• Bounded functionRelated: Uniform limits of bounded functions remain bounded when the approximating sequence is uniformly bounded.

• Convergence of a seriesRelated: Uniform control supports exchanging limits with operations such as integration.

• Asymptotic expansionCompared with: Pointwise asymptotic accuracy need not provide uniform control over a range of inputs.

• Gibbs phenomenonCompared with: The persistent peak prevents uniform convergence near a jump.

• Mathematical analysisRelated: It preserves continuity under limits in situations where pointwise convergence alone may fail.

• Weierstrass approximation theoremBroader topic: The theorem guarantees this stronger form of approximation, not merely pointwise convergence.

• Weierstrass functionRelated: Uniform convergence of the defining series helps establish continuity of the function.

• Squeeze theoremCompared with: Pointwise squeezing at each input limit does not by itself prove uniform convergence.

• Peano existence theoremRelated: Uniform limits let approximate trajectories converge to a candidate solution.

• Uniform boundedness principleCompared with: Uniform convergence is stronger than pointwise control, while the principle derives a different kind of uniformity.

• Abel's theorem (power series)Compared with: Abel's theorem reaches the boundary without assuming uniform convergence on the full interval.

• Approximation theoryRelated: It captures approximation guarantees that hold simultaneously at every point of a domain.

• Banach–Steinhaus theoremCompared with: Uniform convergence controls function values directly, while this theorem derives uniform operator norms from pointwise bounds.

• Hurwitz's theoremCompared with: Hurwitz requires uniform convergence only on compact subsets, not necessarily across the entire domain.

• Runge's theoremRelated: Runge approximation controls the maximum error across the entire compact set.

• Jordan's lemmaRelated: Careful uniform bounds justify taking the large-radius limit of arc integrals.

• Tietze extension theoremRelated: The successive corrections converge uniformly, preserving continuity of their sum.

• Cauchy–Hadamard theoremRelated: Power series converge uniformly on compact subsets strictly inside the radius, not merely pointwise.

• Heine–Cantor theoremCompared with: Its shared idea of global control is distinct from uniform continuity of a single function.

• Gromov–Hausdorff convergenceCompared with: Unlike function convergence, Gromov–Hausdorff convergence compares changing spaces without fixed coordinates.

• Leibniz integral ruleRelated: Uniform control can help justify interchanging a limit-based derivative and an integral.

• Weierstrass M-testNarrower topic: The M-test guarantees this stronger form of convergence for the series’ partial sums.

• Ergodic theoremCompared with: Ergodic theorems generally provide almost-everywhere or norm convergence, not uniform convergence.

• Fejér's theoremRelated: Fejér's conclusion controls approximation error over the entire period at once.

• StabilityCompared with: It is a class-level route to generalization, distinct from algorithm-specific stability.

• Dirichlet–Jordan testCompared with: Pointwise convergence in the test does not imply uniform convergence.

• Glivenko–Cantelli theoremRelated: The theorem controls the largest discrepancy across all thresholds at once.

• Mergelyan's theoremRelated: The theorem guarantees approximation in this global sense, not merely pointwise closeness.

• Abel's inequalityRelated: Uniform bounds on partial sums let Abel estimates support uniform convergence proofs.