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- 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).".
- Arzelà–Ascoli_theorem wikiPageID "596622".
- Arzelà–Ascoli_theorem wikiPageRevisionID "604601645".
- Arzelà–Ascoli_theorem id "2961".
- Arzelà–Ascoli_theorem title "Ascoli–Arzelà theorem".
- 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 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 label "Satz von Arzelà-Ascoli".
- Arzelà–Ascoli_theorem label "Stelling van Arzelà-Ascoli".
- Arzelà–Ascoli_theorem label "Teorema de Arzelà-Ascoli".
- Arzelà–Ascoli_theorem label "Teorema de Arzelá-Ascoli".
- Arzelà–Ascoli_theorem label "Teorema di Ascoli-Arzelà".
- Arzelà–Ascoli_theorem label "Théorème d'Ascoli".
- Arzelà–Ascoli_theorem label "Twierdzenie Arzeli-Ascolego".
- Arzelà–Ascoli_theorem label "Теорема Асколи — Арцела".
- Arzelà–Ascoli_theorem label "阿尔泽拉－阿斯科利定理".
- Arzelà–Ascoli_theorem sameAs Arzel%C3%A0%E2%80%93Ascoli_theorem.
- Arzelà–Ascoli_theorem sameAs Satz_von_Arzelà-Ascoli.
- Arzelà–Ascoli_theorem sameAs Teorema_de_Arzelá-Ascoli.
- Arzelà–Ascoli_theorem sameAs Théorème_d'Ascoli.
- Arzelà–Ascoli_theorem sameAs Teorema_di_Ascoli-Arzelà.
- Arzelà–Ascoli_theorem sameAs Stelling_van_Arzelà-Ascoli.
- Arzelà–Ascoli_theorem sameAs Twierdzenie_Arzeli-Ascolego.
- Arzelà–Ascoli_theorem sameAs Teorema_de_Arzelà-Ascoli.
- Arzelà–Ascoli_theorem sameAs Q1477053.
- Arzelà–Ascoli_theorem sameAs Q1477053.
- Arzelà–Ascoli_theorem wasDerivedFrom Arzelà–Ascoli_theorem?oldid=604601645.