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Equicontinuity: Equicontinuity, Mathematical Analysis, Continuous Function, Neighbourhood (mathematics) -

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2026-03-15
109,28 € 182,14 €

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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 contin ... Täielik kirjeldus

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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[1] 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.

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Kirjastaja OmniScriptum
Väljalaskeaasta 2026
Kaanetüüp Pehme kaanega
EAN 9786131107870
Kirjuta oma arvustus
Te vaatate: Equicontinuity: Equicontinuity, Mathematical Analysis, Continuous Function, Neighbourhood (mathematics)
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109,28 € 182,14 €