equicontinuous at a point

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equicontinuous at a point [¦ē·kwē·kən′tiŋ·yə·wəs at ə ′pöint]

(mathematics)

A family of functions is equicontinuous at a pointxif for any ε > 0 there is a δ > 0 such that, whenever |x-y| < δ, |ƒ(x)-ƒ(y)|<ε for every function ƒ(x) in the family.

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