Kazimierz Kuratowski

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Kazimierz Kuratowski

Kazimierz Kuratowski (born February 2, 1896 in Warsaw , Poland , † June 18, 1980 in Warsaw) was a Polish mathematician and logician.

Kuratowski came from the lawyer Marek Kuratow and from Róża b. Exit Karzewska. He graduated in 1913 the philological Chrzanowski -Gymnasium in Warsaw, and then studied until 1914 in Glasgow in the subject Mathematics . To avoid difficulties with his name, he changed it to Casimir Curatov . After the re-establishment of the Polish University of Warsaw in 1915, he returned there and completed his studies three years later. His doctoral thesis from 1921 comprised two parts:

  1. An axiomatic foundation of the topology by introducing the so-called axiomatics of degrees ( "Sur la notion de l'ensemble fini" , Fundamenta Mathematicae 1, 1920)
  2. The final decision on the problem of irreducible continua that had been the subject of Zygmunt Janiszewski's Paris doctoral thesis . The supervisor of the doctoral thesis was Sierpinski , as the original supervisor, Janiszewski, was no longer alive.

In the autumn of the same year he completed his habilitation at Warsaw University with the solution to a problem from set theory . Originally this came from de la Vallée Poussin , a Belgian mathematician. Two years later he became deputy professor at the second chair for mathematics at Warsaw University and in 1927 took over the third chair for mathematics at the general department of the Polytechnic in Lemberg , in the position of associate professor . He headed this chair until 1933 and was dean twice. After the department was dissolved, he took over the fourth chair for mathematics at Warsaw University in 1934 as a full professor (1934-1935), then he headed the third chair there (1935-1952, with an interruption due to the war). Between 1936 and 1939 he was Secretary of the Mathematical Committee in the Council for Exact and Applied Sciences. During the Second World War he taught at the underground university in Warsaw. From 1929 he was a member of the Warsaw Scientific Society (from 1946 as Vice President of Department 3, from 1949 as Vice President of the Society).

When the Warsaw University reopened in February 1945, he resumed his lecturing activities. In the same year he was appointed a full member of the Polish Academy of Sciences and was its vice-president from 1957 to 1968. Immediately after the end of the Second World War, he was actively involved in rebuilding scientific life in Poland by, among other things, establishing the State Mathematical Institute, which later became the Mathematical Institute of the Polish Academy of Sciences. He was director of this institute from 1948–1968 and was also chairman of the Science Council (1968–1980) and head of the topology department (1948–1980).

He took an active part in the work of the Warsaw Scientific Society and the Polish Mathematical Society, was its long-time chairman and honorary member. He was also the editor of “Fundamenta Mathematicae” , from 1925 its editor-in-chief, of the Bulletin of the Polish Academy of Sciences” , co-creator and editor of the book series “Mathematical Monographs” , in which the most valuable works of representatives of the Warsaw and Lviv mathematical schools were published . He was a member of numerous foreign societies and academies: Royal Society of Edinburgh , Austria, Germany, Hungary, Italy and the Soviet Union.

Kuratowski mainly worked in topology. He created the axiomatics of degrees, also known today as the Kuratowski axiomatics. This forms the basis for the development of the theory of topological spaces in general, and in particular his theory of the irreducible continua between two points. Kuratowski's most important results after World War II include those that established a relationship between topology and the theory of analytic functions, as well as the deep-seated theorems on intersection theory in Euclidean spaces. Together with Stanislaw Ulam , his most gifted student from his time in Lemberg, he developed the concept of quasi-homeomorphism , which formed the starting point for a new area of ​​topological research.

His research in dimension theory , including joint results from Stefan Banach and Alfred Tarski , was continued by numerous successors. The joint work of Kuratowski with Bronisław Knaster in the theory of connected sets brought a comprehensive and exact overview of the corresponding general theory. This in turn could be applied to problems of the intersection theory of the plane, in particular to the corresponding paradoxical examples of connected sets; Mention should be made of the doubly connected Knaster-Kuratowski set .

Kuratowski is the author of the theorem, which is known today as Lemma von Kuratowski-Zorn or Lemma von Zorn , and which was first proven by Kuratowski in 1922 in issue 3 of "Fundamenta Mathematicae" . This lemma has nontrivial applications in the proofs of numerous fundamental theorems. Zorn applied it in 1935 (Bulletin of the American Mathematical Society, 41). The terms that Kuratowski introduced into set theory and topology were permanently included in the literature on these areas. In many cases he was even the creator of the relevant terminology and symbolism.

His post-war work encompassed more or less three fields of research:

  1. The development of the homotopy theory of continuous functions
  2. The construction of the theory of locally connected spaces in higher dimensions
  3. The uniform representation of the intersection theory of Euclidean spaces through arbitrary subsets, based on the properties of continuous transformations of these subsets.

Among the more than 170 scientific publications, his monographs and textbooks deserve special mention, including his "Topologie" (vol. 1 1933, vol. 2 1950), a fundamental work that was also published in English and Russian, his "set theory" (jointly with Mostowski, published 1952, translations into English and Russian), as well as his "Introduction to Set Theory and Topology" (published 1952, translations into English, French, Spanish, Bulgarian). He was also the author of the popular science report “Half a Century of Polish Mathematics 1920-1970” (1973) and the posthumously published “Notes on the Autobiography” (1981), which his daughter Zofia brought to print.

He represented Polish mathematics in the International Mathematical Union , of which he was vice-president from 1963 to 1966, represented it at numerous international congresses and gave lectures in dozen universities around the world. He was an honorary doctorate from the Universities of Glasgow, Prague, Wrocław and Paris. He was the recipient of the highest state honors, including the gold medal of the Czechoslovak Academy of Sciences and the Copernicus Medal of the Polish Academy of Sciences .

Source: Text by Zofia Pawlikowska-Brozek.

This biography is an entry in the “Encyclopedia of Polish Mathematicians”, Proszynski and S-ka (in preparation).

(This text is a translation from the Polish Wikipedia.)

See also

Kuratowski's theorem

Web links

Individual evidence

  1. ^ IN Sneddon, Kazimierz Kuratowski Hon. FRSE, Yearbook of the Royal Society of Edinburgh Session 1980-81 (1982), 40-47.