Béla Kerékjártó

Béla Kerékjártó (1 October 1898, in Budapest – 26 June 1946, in Gyöngyös) was a Hungarian mathematician who wrote numerous articles on topology.

Béla Kerékjártó

Kerékjártó earned his Ph.D. degree from the University of Budapest in 1920. He taught at the Faculty of Sciences of the University of Szeged 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."[1]

Life and career

In 1923, Kerékjártó published one of the first books on Topology, which was reviewed by Solomon Lefschetz in 1925.[2] Hermann Weyl wrote that this book completely changed his views of the subject.

In 1919 he published a theorem on periodic homeomorphisms of the disc and the sphere.[3] A claim to priority to the result was made by L. E. J. Brouwer, and the subject was revisited by Samuel Eilenberg in 1934.[4] A modern treatment of Kerékjártó's theorem has been presented by Adrian Constantin and Boris Kolev.[5]

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.[6]

In 1938 he returned to Budapest to teach at Eötvös Loránd University.

Kerékjártó proved that the sphere is the only compact surface that admits a 3-transitive topological group in 1941.[7]

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
gollark: You could do it both ways I guess, perhaps with a switch.
gollark: If you tracked clicks on each internal link you could estimate connection importance that way. Or manually specify importance levels. Or have something to emphasise links between big clusters.
gollark: > it seems like you're talking more about an API?Yes, I think the ability to do that might be more useful to (some) external services than having UI in Athens itself.> Dokuwiki does seem interesting thoughIt's a pretty good selfhosted wiki engine. It doesn't have knowledge-graph-y features because it was mostly made before that became a topic of interest, but does have... search, links, somewhat okay formatting, and many plugins. I currently run an instance because it seemed the best available stable thing when I was setting up things and it is quite hard to migrate now.
gollark: Sorry if I'm explaining this somewhat badly. I can probably clarify. I mean something like this (https://www.dokuwiki.org/plugin:struct) but without necessarily having to define a schema somewhere. I think this would be good for a few categories of thing, such as, say, exporting a list of cards (defined in notes) into a spaced repetition system. Possibly calendar events/reminders too, but you'd probably want a way to remove expired ones.
gollark: Regarding integration/plugins (I didn't see this being thought of here before or on github when I did a search, but my queries might have been bad): a nice/general way to integrate some types of external service without having to integrate per-service code could be to have a way to have blocks containing arbitrary machine-readable data (with a nice UI to edit it) and a type field, and an API to find all/all recent blocks with a given type.

References
  1. M. Bognár & Á. Csázár, "Topology" (pp 9 to 25) in A Panorama of Hungarian Mathematics in the Twentieth Century, János Horváth (editor) Bolyai Society Mathematical Studies 14, link from Google Books
  2. Solomon Lefschetz (1925) Review: Vorlesungen über Topologie, Bulletin of the American Mathematical Society 31(3-4):176
  3. B. Kerekjarto (1919) "Uber die periodische transformationen der Kreisscheibe und die Kugelflasche", Mathematische Annalen 80:36–8
  4. Samuel Eilenberg (1934) "Sur les transformationes periodique de la surface de la sphere", Fundamentica Mathematica 22:28–44
  5. Adrian Constantin and Boris Kolev (2003) The theorem of Kerekjarto on periodic homeomorphisms of the disc and sphere from Internet Archive
  6. "A short history of the Bolyai Institute", at the János Bolyai Mathematical Institute
  7. Béla Kerékjártó (1941) "Sur le caractère topologique du groupe homographique de la sphère.", Acta Mathematica 74:311–41 MR0013311
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