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Cesare Arzelà (6 March 1847–15 March 1912) was an Italian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who taught at the
University of Bologna The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the ...
and is recognized for his contributions in the theory of functions, particularly for his characterization of
sequences In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is call ...
of
continuous function In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as '' discontinuities''. More preci ...
s, generalizing the one given earlier by Giulio Ascoli in the
Arzelà–Ascoli theorem 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 inte ...
.


Life

He was a pupil of the Scuola Normale Superiore of
Pisa Pisa ( ; ) is a city and ''comune'' (municipality) in Tuscany, Central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for the Leaning Tow ...
where he graduated in 1869. Arzelà came from a poor household; therefore he could not start his study until 1871, when he studied in Pisa under
Enrico Betti Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations ...
and Ulisse Dini. He was working in
Florence Florence ( ; ) is the capital city of the Italy, Italian region of Tuscany. It is also the most populated city in Tuscany, with 362,353 inhabitants, and 989,460 in Metropolitan City of Florence, its metropolitan province as of 2025. Florence ...
(from 1875) and in 1878 obtained the Chair of Algebra at the
University of Palermo The University of Palermo () is a public university, public research university in Palermo, Italy. It was founded in 1806, and is currently organized in 12 Faculties. History The University of Palermo was officially founded in 1806, although it ...
. After that, he became a professor in 1880 at the
University of Bologna The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the ...
at the Department of analysis. He conducted research in the field of theory of functions. His most famous student was
Leonida Tonelli Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian people, Italian mathematician, noted for proving Fubini's theorem#Tonelli's theorem for non-negative measurable functions, Tonelli's theorem, a variation of Fubini's theorem, and f ...
. In 1889 he generalized the Ascoli theorem to
Arzelà–Ascoli theorem 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 inte ...
, an important
theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
in the theory of functions. He was a member of the
Accademia Nazionale dei Lincei The (; literally the "Academy of the Lynx-Eyed"), anglicised as the Lincean Academy, is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in ...
, and of several other academies.


Works

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See also

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Total variation In mathematics, the total variation identifies several slightly different concepts, related to the (local property, local or global) structure of the codomain of a Function (mathematics), function or a measure (mathematics), measure. For a real ...


Further reading

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External links

* 1847 births 1912 deaths 20th-century Italian mathematicians Italian mathematical analysts Academic staff of the University of Palermo {{Italy-mathematician-stub