- Kazimierz Kuratowski
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Kazimierz Kuratowski (
Warsaw ,February 2 ,1896 –June 18 ,1980 ) was a Polishmathematician andlogician .Biography
Kuratowski was born a subject of
Tsar istRussia . In 1913, he enrolled in an engineering course at theUniversity of Glasgow inScotland , in part because he did not wish to study in Russian. He had completed only one year of study when the outbreak ofWorld War I precluded any further enrollment. In 1915, Kuratowski restarted his university education at theUniversity 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 atWarsaw University . In 1945 he became a member of thePolish Academy of Learning , and in 1952 of thePolish 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 includeAndrzej 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 andWacław Sierpiński he provided most of the theory concerningPolish space s [See for instance the "Kuratowski theorem" in the Standard Borel spaces and Kuratowski theorems section of the article "Borel algebra".] (that are indeed named after these mathematicians and their legacy). His contributions tomathematics also include:
* a characterization ofHausdorff space s in terms of what are now calledKuratowski closure axioms ;
* proof of theKuratowski-Zorn lemma ;
* ingraph theory , the characterization ofplanar graph s now known asKuratowski's theorem ;
* identification of theordered pair x,y) with the set x}, {x,y}}.
* the introduction of theTarski-Kuratowski algorithm .
*Kuratowski's closure-complement problem
*Kuratowski's free set theorem
*Kuratowski convergence of subsets of metric spacesee also
*
Scottish Café 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
* [http://matwbn.icm.edu.pl/kstresc.php?tom=20&wyd=10&jez= TOPOLOGIE I, "Espaces Métrisables, Espaces Complets"] "Monografie Matematyczne" series, vol. 20, Polish Mathematical Society, Warszawa-Lwów, 1948.
* [http://matwbn.icm.edu.pl/kstresc.php?tom=21&wyd=10&jez= TOPOLOGIE II, "Espaces Compacts, Espaces Connexes, Plan Euclidien"] "Monografie Matematyczne" series, vol. 21, Polish Mathematical Society, Warszawa-Lwów, 1950.
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* [http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=24546 Kazimierz Kuratowski] in theMathematics Genealogy Project Notes
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