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The 35 pages that link to Continuity, each with the reason it gives.

• Augustin-Louis CauchyRelated: Cauchy gave continuity a precise formulation using infinitesimal changes.

• Limit of a functionRelated: Continuity is precisely the case where limiting behavior matches the actual value.

• Real analysisRelated: Continuity is characterized by limits and preserved under many analytic operations.

• CalculusRelated: Continuity helps establish when calculus operations behave predictably.

• DifferentiabilityRelated: Differentiability implies continuity, but continuity alone does not imply differentiability.

• Fixed pointRelated: Continuity is a key hypothesis in major fixed-point existence theorems.

• Fundamental theorem of calculusRelated: Continuity guarantees the integrand's accumulation function has the stated derivative.

• Lipschitz continuityNarrower topic: Every Lipschitz function is continuous, but continuity alone gives no linear rate.

• Picard–Lindelöf theoremRelated: Continuity in the independent variable and state is part of the theorem’s hypotheses.

• Uniform continuityCompared with: Ordinary continuity allows the input bound to depend on the point.

• Bernard BolzanoRelated: Bolzano formulated a precise account of continuity central to his analysis.

• Mathematical analysisBroader topic: Continuity formalizes when small changes in input guarantee small changes in output.

• Mean value theoremNarrower topic: Continuity on the closed interval is an essential hypothesis of the theorem.

• Weierstrass functionRelated: Continuity is the regularity the function retains at every point.

• Rolle's theoremNarrower topic: Continuity on the closed interval guarantees extrema are attained.

• Darboux's theoremRelated: The theorem is striking because derivative continuity is not required.

• Squeeze theoremRelated: Continuity supplies many outer functions whose limits are easy to calculate.

• Basis (topology)Related: Checking inverse images of basis members suffices to establish continuity.

• Indeterminate formRelated: Continuity can make direct substitution sufficient, bypassing indeterminate forms.

• L'Hôpital's ruleRelated: Continuity near the limiting point is part of common hypotheses for the theorem.

• Peano existence theoremRelated: Continuity of the differential equation’s right-hand side is the theorem’s key hypothesis.

• Hyperreal numberRelated: For real functions, continuity can be characterized by sending infinitesimally close inputs to infinitesimally close outputs.

• One-sided limitRelated: One-sided limits test continuity at endpoints and across piecewise definitions.

• Real-valued functionRelated: Real-valued functions can be classified by where their outputs change continuously.

• Differentiable functionNarrower topic: Differentiability implies continuity, but continuity alone does not ensure differentiability.

• Zeno's paradoxesRelated: Accounts of continuous space and time shape how the paradoxes' intervals are interpreted.

• Heine–Cantor theoremNarrower topic: Continuity supplies the local control required by the theorem.

• Cauchy's mean value theoremNarrower topic: Both functions must be continuous through the interval, including its endpoints.

• Bolzano's theoremNarrower topic: Continuity prevents the function from changing signs without taking the value zero.

• Morera's theoremRelated: Continuity is essential in Morera's hypothesis and cannot generally be omitted.

• Denjoy–Luzin theoremCompared with: Approximate continuity is weaker: it permits exceptional nearby points so long as they have density zero.

• Dini testNarrower topic: The Dini condition strengthens local continuity with a quantitative oscillation bound.

• Function of a real variableRelated: It captures when a function’s graph has no breaks in the relevant region.

• Function of several real variablesRelated: Continuity extends to tuples of inputs using limits in several dimensions.

• Symmetry of second derivativesRelated: Continuity of the mixed partials is a sufficient condition for their equality.