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- Equicontinuity abstract "In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions.The equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of C(X), the space of continuous functions on a compact Hausdorff space X, is compact if and only if it is closed, pointwise bounded and equicontinuous. As a corollary, a sequence in C(X) is uniformly convergent if and only if it is equicontinuous and converges pointwise to a function (not necessarily continuous a-priori). In particular, the limit of an equicontinuous pointwise convergent sequence of continuous functions fn on either metric space or locally compact space is continuous. If, in addition, fn are holomorphic, then the limit is also holomorphic.The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between Banach spaces is equicontinuous.".
- Equicontinuity wikiPageID "460642".
- Equicontinuity wikiPageRevisionID "601660040".
- Equicontinuity hasPhotoCollection Equicontinuity.
- Equicontinuity id "p/e035990".
- Equicontinuity title "Equicontinuity".
- Equicontinuity subject Category:Continuous_mappings.
- Equicontinuity subject Category:Mathematical_analysis.
- Equicontinuity type Abstraction100002137.
- Equicontinuity type ContinuousMappings.
- Equicontinuity type Function113783816.
- Equicontinuity type MathematicalRelation113783581.
- Equicontinuity type Relation100031921.
- Equicontinuity comment "In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein.".
- Equicontinuity label "Equicontinuidad".
- Equicontinuity label "Equicontinuidade".
- Equicontinuity label "Equicontinuity".
- Equicontinuity label "Equicontinuità".
- Equicontinuity label "Gleichgradige Stetigkeit".
- Equicontinuity label "Équicontinuité".
- Equicontinuity label "Равностепенная непрерывность".
- Equicontinuity label "同程度連続".
- Equicontinuity label "等度连续".
- Equicontinuity sameAs Gleichgradige_Stetigkeit.
- Equicontinuity sameAs Equicontinuidad.
- Equicontinuity sameAs Équicontinuité.
- Equicontinuity sameAs Equicontinuità.
- Equicontinuity sameAs 同程度連続.
- Equicontinuity sameAs 동등연속.
- Equicontinuity sameAs Equicontinuidade.
- Equicontinuity sameAs m.02c8gk.
- Equicontinuity sameAs Q249092.
- Equicontinuity sameAs Q249092.
- Equicontinuity sameAs Equicontinuity.
- Equicontinuity wasDerivedFrom Equicontinuity?oldid=601660040.
- Equicontinuity isPrimaryTopicOf Equicontinuity.