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- Arzel%C3%A0%E2%80%93Ascoli_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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- Arzel%C3%A0%E2%80%93Ascoli_theorem id "2961".
- Arzel%C3%A0%E2%80%93Ascoli_theorem title "Ascoli–Arzelà theorem".
- Arzel%C3%A0%E2%80%93Ascoli_theorem subject Category:Articles_containing_proofs.
- Arzel%C3%A0%E2%80%93Ascoli_theorem subject Category:Compactness_theorems.
- Arzel%C3%A0%E2%80%93Ascoli_theorem subject Category:Continuous_mappings.
- Arzel%C3%A0%E2%80%93Ascoli_theorem subject Category:Theorems_in_functional_analysis.
- Arzel%C3%A0%E2%80%93Ascoli_theorem subject Category:Topology_of_function_spaces.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Abstraction100002137.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Communication100033020.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type CompactnessTheorems.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type ContinuousMappings.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Function113783816.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type MathematicalRelation113783581.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Message106598915.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Proposition106750804.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Relation100031921.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Statement106722453.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type Theorem106752293.
- Arzel%C3%A0%E2%80%93Ascoli_theorem type TheoremsInFunctionalAnalysis.
- Arzel%C3%A0%E2%80%93Ascoli_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.".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Arzelà–Ascoli theorem".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Satz von Arzelà-Ascoli".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Stelling van Arzelà-Ascoli".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Teorema de Arzelà-Ascoli".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Teorema de Arzelá-Ascoli".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Teorema di Ascoli-Arzelà".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Théorème d'Ascoli".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Twierdzenie Arzeli-Ascolego".
- Arzel%C3%A0%E2%80%93Ascoli_theorem label "Теорема Асколи — Арцела".
- Arzel%C3%A0%E2%80%93Ascoli_theorem sameAs m.02tt90.
- Arzel%C3%A0%E2%80%93Ascoli_theorem sameAs Arzelà–Ascoli_theorem.
- Arzel%C3%A0%E2%80%93Ascoli_theorem wasDerivedFrom Arzelà–Ascoli_theorem?oldid=644024479.
- Arzel%C3%A0%E2%80%93Ascoli_theorem isPrimaryTopicOf Arzelà–Ascoli_theorem.