Béla Kerékjártó (1 October 1898, in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

– 26 June 1946, in

Gyöngyös Gyöngyös (; german: Gengeß) is a town in Heves county in Hungary, east of Budapest. Situated at the foot of the Sár-hegy and Mátra mountains, it is the home of numerous food production plants, including milk production and sausage factori ...

) was a Hungarian mathematician who wrote numerous articles on

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. Kerékjártó earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

degree from the

University of Budapest A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

in 1920. He taught at the

Faculty of Sciences Science education is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process (the scientific method), some ...

of the

University of Szeged , mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 m ...

starting in 1922. In 1921 he introduced his program with a talk "On topological fundamentals of analysis and geometry" where he advocated that "complex analysis should be built with instruments of topology without metric elements such as length and area."

Life and career

In 1923, Kerékjártó published one of the first books on Topology, which was reviewed by

Solomon Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear o ...

in 1925. Hermann Weyl wrote that this book completely changed his views of the subject. In 1919 he published a theorem on periodic

homeomorphism In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomor ...

s of the disc and the sphere. A claim to priority to the result was made by

L. E. J. Brouwer Luitzen Egbertus Jan Brouwer (; ; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and compl ...

, and the subject was revisited by

Samuel Eilenberg Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to ...

in 1934. A modern treatment of Kerékjártó's theorem has been presented by Adrian Constantin and Boris Kolev. Kerékjártó was appointed head of the Department of Geometry and Descriptive Geometry at the János Bolyai Mathematical Institute of the University of Szeged in 1925. In 1938 he returned to Budapest to teach at Eötvös Loránd University. Kerékjártó proved that the

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...

is the only

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

that admits a 3-transitive

topological group In mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two st ...

in 1941.Béla Kerékjártó (1941) "Sur le caractère topologique du groupe homographique de la sphère.", Acta Mathematica 74:311–41

Books

* 1923: ''Vorlesungen über Topologie Bd.1 Flächentopologie'', Grundlehren der mathematischen Wissenschaften, Springer Verlag * 1955: ''Les Fondements de la Géométrie. Bd.1. La construction élémentaire de la géométrie euclidienne'', Gauthier-Villars. * 1966: ''Les Fondaments de la Géométrie Bd.2, Geometrie projective'', Gauthiers-Villars.

Articles

* 1919: "A torus periodikus transformitioirol", Math. Term. tad. Értesitiö 39:213–9. * 1930: "Geometrische Theorie der zweigliedrigen kontinuierlichen Gruppen",

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (English: ''Reports from the Mathematical Seminar of the University of Hamburg'') is a peer-reviewed mathematics journal published by Springer Science+Business Media. It publishes articles on pure mathematics and is scientifically coordinated by ...

8:107–14. * 1934: "Sur la character topologique des representationes conformes", Comptes rendus 198:317–20. * 1934: "Über reguläre Abbildungen von Flächen auf sich",

Acta Scientiarum Mathematicarum ''Acta Scientiarum Mathematicarum'' is a Hungarian mathematical journal published by the János Bolyai Mathematical Institute (University of Szeged). It was established by Alfréd Haar and Frigyes Riesz in 1922. The current editor-in-chief is Lajo ...

7:65–85 & 206. * 1934: "Topologische Characterisierung der linearen Abbildungen",

6:235–62, esp. 250. * 1940: "Sur les inversions dans un groupe commutative", Comptes rendus 210:288. * 1940: "Sur le group des homographies et des antihomographies d’une variable complexe",

Commentarii Mathematici Helvetici The ''Commentarii Mathematici Helvetici'' is a quarterly peer-reviewed scientific journal in mathematics. The Swiss Mathematical Society started the journal in 1929 after a meeting in May of the previous year. The Swiss Mathematical Society sti ...

13:68–82. * 1941: "Sur les groups compact de transformations topologique des surfaces", Acta Mathematica 74:129–73.

References

External links

* {{DEFAULTSORT:Kerekjarto, Bela 20th-century Hungarian mathematicians Topologists University of Szeged faculty Mathematicians from Budapest 1898 births 1946 deaths Austro-Hungarian mathematicians Eötvös Loránd University alumni Eötvös Loránd University faculty