Béla Kerékjártó (1 October 1898, in

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

– 26 June 1946, in

Gyöngyös Gyöngyös is a town in Heves County, Hungary, beside of the Gyöngyös creek, under the Mátra mountain ranges. As of 2022 census, it has a population of 27,957 (see Demographics). The town is located 8.4 km from the M3 motorway and 80.8 km ...

) was a Hungarian mathematician who wrote numerous articles on

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. Kerékjártó earned his Ph.D. degree from the

University of Budapest A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

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 The University of Szeged () is a Public university, public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by ...

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 (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equatio ...

in 1925.

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

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

homeomorphism In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function ...

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

L. E. J. Brouwer Luitzen Egbertus Jan "Bertus" Brouwer (27 February 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the ...

, 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 Eötvös Loránd University (, ELTE, also known as ''University of Budapest'') is a Hungarian public research university based in Budapest. Founded in 1635, ELTE is one of the largest and most prestigious public higher education institutions in ...

. Kerékjártó proved that the

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

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, a type of agreement used by U.S. states * Blood compact, an ancient ritual of the Philippines * Compact government, a t ...

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 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 structures ...

in 1941.Béla Kerékjártó (1941) "Sur le caractère topologique du groupe homographique de la sphère.",

Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

74:311–41

Books

* 1923: ''Vorlesungen über Topologie Bd.1 Flächentopologie'', Grundlehren der mathematischen Wissenschaften,

Springer Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

* 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 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 7:65–85 & 206. * 1934: "Topologische Characterisierung der linearen Abbildungen", Acta Scientiarum Mathematicarum 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 (SMG) started the journal in 1929 after a meeting in May of the previous year. The Swiss Mathematical Socie ...

13:68–82. * 1941: "Sur les groups compact de transformations topologique des surfaces",

74:129–73.

References

External links

* {{DEFAULTSORT:Kerekjarto, Bela 20th-century Hungarian mathematicians Topologists Academic staff of the University of Szeged Mathematicians from Budapest 1898 births 1946 deaths Mathematicians from Austria-Hungary Eötvös Loránd University alumni Academic staff of Eötvös Loránd University