Kazimierz Kuratowski (Warsaw, February 2, 1896–June 18, 1980) was a Polish mathematician and logician.
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Biography
Kuratowski was born a subject of Tsarist Russia. In 1913, he enrolled in an engineering course at the University of Glasgow in Scotland, in part because he did not wish to study in Russian. He had completed only one year of study when the outbreak of World War I precluded any further enrollment. In 1915, Kuratowski restarted his university education at the University of Warsaw, this time in mathematics, obtaining the Ph.D. in 1921.
He was appointed professor of mathematics in 1927 at the Lwów Polytechnic in Lwów, Poland, and from 1934 at Warsaw University. In 1945 he became a member of the Polish Academy of Learning, and in 1952 of the Polish Academy of Sciences. From 1948 until 1967 he was director of the Institute of Mathematics of the Polish Academy of Sciences, and he was also a long-time chairman of the Polish and International Mathematics Societies. His students include Andrzej Mostowski.
Kazimierz Kuratowski was one of a celebrated group of Polish mathematicians who would meet at Lwów's Kawiarnia Szkocka (Scottish Café).
Research
Kuratowski's research was mainly focused on abstract topological and metric structures. With Alfred Tarski and Wacław Sierpiński he provided most of the theory concerning Polish spaces[1] (that are indeed named after these mathematicians and their legacy). His contributions to mathematics also include:
- a characterization of Hausdorff spaces in terms of what are now called Kuratowski closure axioms;
- proof of the Kuratowski-Zorn lemma;
- in graph theory, the characterization of planar graphs now known as Kuratowski's theorem;
- identification of the ordered pair (x,y) with the set {{x},{x,y}}.
- the introduction of the Tarski-Kuratowski algorithm.
- Kuratowski's closure-complement problem
- Kuratowski's free set theorem
- Kuratowski convergence of subsets of metric spaces
- the Kuratowski, Ryll-Nardzewski measurable selection theorem
See also
References
- Kazimierz Kuratowski, A Half Century of Polish Mathematics: Remembrances and Reflections, Oxford, Pergamon Press, 1980, ISBN 0-08-023046-6.
- Karol Borsuk, "On the Achievements of Prof. Dr. Kazimierz Kuratowski in Topology" (in Polish), Wiadomości matematyczne, vol. 2, no. 3, 1960, pp. 231-237.
External links
- TOPOLOGIE I, Espaces Métrisables, Espaces Complets Monografie Matematyczne series, vol. 20, Polish Mathematical Society, Warszawa-Lwów, 1948.
- TOPOLOGIE II, Espaces Compacts, Espaces Connexes, Plan Euclidien Monografie Matematyczne series, vol. 21, Polish Mathematical Society, Warszawa-Lwów, 1950.
- O'Connor, John J.; Robertson, Edmund F., "Kazimierz Kuratowski", MacTutor History of Mathematics archive, http://www-history.mcs.st-andrews.ac.uk/Biographies/Kuratowski.html.
- Kazimierz Kuratowski in the Mathematics Genealogy Project
Notes
- ^ See for instance the Kuratowski theorem in the Standard Borel spaces and Kuratowski theorems section of the article Borel algebra.
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