Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Arzelà–Ascoli_theorem> ?p ?o }
- Arzelà–Ascoli_theorem abstract "The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary differential equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis.The notion of equicontinuity was introduced at around the same time by Ascoli (1883–1884) and Arzelà (1882–1883). A weak form of the theorem was proven by Ascoli (1883–1884), who established the sufficient condition for compactness, and by Arzelà (1895), who established the necessary condition and gave the first clear presentation of the result. A further generalization of the theorem was proven by Fréchet (1906), to sets of real-valued continuous functions with domain a compact metric space (Dunford & Schwartz 1958, p. 382). Modern formulations of the theorem allow for the domain to be compact Hausdorff and for the range to be an arbitrary metric space. More general formulations of the theorem exist that give necessary and sufficient conditions for a family of functions from a compactly generated Hausdorff space into a uniform space to be compact in the compact-open topology. Kelley (1991, page 234).".
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- Arzelà–Ascoli_theorem wikiPageWikiLink Banach_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Bolzano–Weierstrass_theorem.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Category:Articles_containing_proofs.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Complex_analysis.
- Arzelà–Ascoli_theorem wikiPageWikiLink Continuous_function.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Derivative.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Equicontinuity.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Fréchet–Kolmogorov_theorem.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Infimum_and_supremum.
- Arzelà–Ascoli_theorem wikiPageWikiLink Interval_(mathematics).
- Arzelà–Ascoli_theorem wikiPageWikiLink Linear_map.
- Arzelà–Ascoli_theorem wikiPageWikiLink Lipschitz_continuity.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Mathematical_analysis.
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- Arzelà–Ascoli_theorem wikiPageWikiLink Metric_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Modulus_of_continuity.
- Arzelà–Ascoli_theorem wikiPageWikiLink Montels_theorem.
- Arzelà–Ascoli_theorem wikiPageWikiLink Necessity_and_sufficiency.
- Arzelà–Ascoli_theorem wikiPageWikiLink Ordinary_differential_equation.
- Arzelà–Ascoli_theorem wikiPageWikiLink Oscillation_(mathematics).
- Arzelà–Ascoli_theorem wikiPageWikiLink Peano_existence_theorem.
- Arzelà–Ascoli_theorem wikiPageWikiLink Peter–Weyl_theorem.
- Arzelà–Ascoli_theorem wikiPageWikiLink Rational_number.
- Arzelà–Ascoli_theorem wikiPageWikiLink Rational_point.
- Arzelà–Ascoli_theorem wikiPageWikiLink Real_line.
- Arzelà–Ascoli_theorem wikiPageWikiLink Real_number.
- Arzelà–Ascoli_theorem wikiPageWikiLink Relatively_compact_subspace.
- Arzelà–Ascoli_theorem wikiPageWikiLink Separable_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Sequence.
- Arzelà–Ascoli_theorem wikiPageWikiLink Smoothness.
- Arzelà–Ascoli_theorem wikiPageWikiLink Sobolev_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Springer_Science+Business_Media.
- Arzelà–Ascoli_theorem wikiPageWikiLink Subsequence.
- Arzelà–Ascoli_theorem wikiPageWikiLink Topological_vector_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Uniform_boundedness.
- Arzelà–Ascoli_theorem wikiPageWikiLink Uniform_convergence.
- Arzelà–Ascoli_theorem wikiPageWikiLink Uniform_norm.
- Arzelà–Ascoli_theorem wikiPageWikiLink Uniform_space.
- Arzelà–Ascoli_theorem wikiPageWikiLink Uniformly_Cauchy_sequence.
- Arzelà–Ascoli_theorem wikiPageWikiLinkText "Arzelà–Ascoli theorem".
- Arzelà–Ascoli_theorem id "2961".
- Arzelà–Ascoli_theorem title "Ascoli–Arzelà theorem".
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- Arzelà–Ascoli_theorem subject Category:Articles_containing_proofs.
- Arzelà–Ascoli_theorem subject Category:Compactness_theorems.
- Arzelà–Ascoli_theorem subject Category:Continuous_mappings.
- Arzelà–Ascoli_theorem subject Category:Theorems_in_functional_analysis.
- Arzelà–Ascoli_theorem subject Category:Topology_of_function_spaces.
- Arzelà–Ascoli_theorem hypernym Result.
- Arzelà–Ascoli_theorem type Diacritic.
- Arzelà–Ascoli_theorem type Function.
- Arzelà–Ascoli_theorem type Mapping.
- Arzelà–Ascoli_theorem type Proof.
- Arzelà–Ascoli_theorem type Redirect.
- Arzelà–Ascoli_theorem type Source.
- Arzelà–Ascoli_theorem type Theorem.
- Arzelà–Ascoli_theorem comment "The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions.".
- Arzelà–Ascoli_theorem label "Arzelà–Ascoli theorem".
- Arzelà–Ascoli_theorem sameAs Q1477053.
- Arzelà–Ascoli_theorem sameAs Satz_von_Arzelà-Ascoli.
- Arzelà–Ascoli_theorem sameAs Teorema_de_Arzelá-Ascoli.
- Arzelà–Ascoli_theorem sameAs Thxc3xa9orxc3xa8me_dAscoli.