Cesare Arzelà (1847 to 1912) was an Italian mathematician who worked on the theory of functions of a real variable. A pupil of the Scuola Normale Superiore of Pisa, he graduated there in 1869 and studied under Enrico Betti and Ulisse Dini before teaching in Florence, then holding the chair of algebra at the University of Palermo from 1878 and a professorship at the University of Bologna from 1880. He is recognised for characterising sequences of continuous functions, generalising an earlier result of Giulio Ascoli into the Arzelà-Ascoli theorem, which he proved in 1889. His most famous student at Bologna was Leonida Tonelli, and he belonged to the Accademia Nazionale dei Lincei and several other academies.
Facts
Defining ContributionProved the Ascoli-Arzelà theorem on uniformly convergent subsequences of equicontinuous functions 2 Connections
In Branch
Source Cesare Arzelà (Wikipedia)
Mentored By
Source Cesare Arzelà (Wikipedia)
Principal Result
Source Cesare Arzelà (Wikipedia)
Proofs Credited
Source ProofWiki: Arzelà-Ascoli Theorem
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Source Cesare Arzelà (Wikipedia)Lead, nationalityQuote, Lead, nationality
was an Italian mathematician who taught at the University of Bologna
Sources
1. Cesare Arzelà (Wikipedia)
Lead, dates
Cesare Arzelà (6 March 1847-15 March 1912)
Life, first sentence
He was a pupil of the Scuola Normale Superiore of Pisa
Lead, nationality
was an Italian mathematician who taught at the University of Bologna
In Branch: Real Analysis, Lead, field of work
particularly for his characterization of sequences of continuous functions
Mentored By: Enrico Betti, Life, studies in Pisa
when he studied in Pisa under Enrico Betti and Ulisse Dini
Principal Result: Arzela-Ascoli Theorem, Lead, Arzela-Ascoli theorem
in the Arzelà-Ascoli theorem
View the Source2. MacTutor History of Mathematics: Cesare Arzelà (MacTutor)
MacTutor History of MathematicsBiography, the 1895 paper on functions of linesQuote, Biography, the 1895 paper on functions of lines
He proved the result now known as the Ascoli-Arzelà theorem on the existence of a uniformly convergent subsequence in every sequence of equilimited and equicontinuous functions.
ProofWiki: Arzelà-Ascoli Theorem
ProofWikiProofs Credited: Arzela-Ascoli Theorem, Lead sentenceQuote, Proofs Credited: Arzela-Ascoli Theorem, Lead sentence
The notion of equicontinuity was introduced in the late 19th century by the Italian mathematicians Cesare Arzelà and Giulio Ascoli.
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