KnowraContinuityLinked fromLinked fromThe 35 pages that link to Continuity, each with the reason it gives.All 35Broader topic 1Related 24Narrower topic 8Compared with 2Lipschitz continuityNarrower topic: Every Lipschitz function is continuous, but continuity alone gives no linear rate.Mean value theoremNarrower topic: Continuity on the closed interval is an essential hypothesis of the theorem.Rolle's theoremNarrower topic: Continuity on the closed interval guarantees extrema are attained.Differentiable functionNarrower topic: Differentiability implies continuity, but continuity alone does not ensure differentiability.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.Dini testNarrower topic: The Dini condition strengthens local continuity with a quantitative oscillation bound.