Cesare Arzelà
Encyclopedia
Cesare Arzelà was an Italian
mathematician
who taught at the University of Bologna
and is recognized for his contributions in the theory of functions, particularly for his characterization of sequences of continuous function
s, generalizing the one given earlier by Giulio Ascoli
in the famous Arzelà-Ascoli theorem
.
where he graduated in 1869. Arzela came from a poor household; therefore he could not start his study until 1871, when he studied in Pisa under Enrico Betti
and Ulisse Dini.
He was working in Florence
(from 1875) and in 1878 obtained the Chair of Algebra at the University of Palermo
.
After that he became a professor in 1880 at the University of Bologna
at the department of analysis. He conducted research in the field of theory of functions. His most famous student was Leonida Tonelli
.
In 1889 he generalized the Ascoli
theorem to Arzelà–Ascoli theorem, an important theorem
in theory of functions.
He was a member of the Accademia Nazionale dei Lincei, and of several other academies.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who taught at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
and is recognized for his contributions in the theory of functions, particularly for his characterization of sequences of continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
s, generalizing the one given earlier by Giulio Ascoli
Giulio Ascoli
Giulio Ascoli was an Italian mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868.In 1872 he became Professor of Algebra and Calculus of the Politecnico di Milano University...
in the famous Arzelà-Ascoli theorem
Arzelà-Ascoli theorem
In mathematics, the Arzelà–Ascoli theorem of functional analysis gives necessary and sufficient conditions to decide whether every subsequence of a given sequence of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition...
.
Life
He was a pupil of the Scuola Normale Superiore of PisaPisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
where he graduated in 1869. Arzela came from a poor household; therefore he could not start his study until 1871, when he studied in Pisa under Enrico Betti
Enrico Betti
-External links:...
and Ulisse Dini.
He was working in Florence
Florence
Florence is the capital city of the Italian region of Tuscany and of the province of Florence. It is the most populous city in Tuscany, with approximately 370,000 inhabitants, expanding to over 1.5 million in the metropolitan area....
(from 1875) and in 1878 obtained the Chair of Algebra at the University of Palermo
University of Palermo
The University of Palermo is a university located in Palermo, Italy, and founded in 1806. It is organized in 12 Faculties.-History:The University of Palermo was officially founded in 1806, although its earliest roots date back to 1498 when medicine and law were taught there...
.
After that he became a professor in 1880 at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
at the department of analysis. He conducted research in the field of theory of functions. His most famous student was Leonida Tonelli
Leonida Tonelli
Leonida Tonelli was an Italian mathematician, most noted for creating Tonelli's theorem, usually considered a forerunner to Fubini's theorem.-External links:...
.
In 1889 he generalized the Ascoli
Giulio Ascoli
Giulio Ascoli was an Italian mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868.In 1872 he became Professor of Algebra and Calculus of the Politecnico di Milano University...
theorem to Arzelà–Ascoli theorem, an important theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
in theory of functions.
He was a member of the Accademia Nazionale dei Lincei, and of several other academies.