Kazimierz Kuratowski

Kazimierz Kuratowski (Polish pronunciation:

After World War II, Kuratowski was actively involved in the rebuilding of scientific life in Poland. He helped to establish the State Mathematical Institute, which was incorporated into the Polish Academy of Sciences in 1952. From 1948 until 1967 Kuratowski was director of the Institute of Mathematics of the Polish Academy of Sciences, and was also a long-time chairman of the Polish and International Mathematics Societies. He served as vice-president of the International Mathematical Union (1963–1966) as well as president of the Scientific Council of the State Institute of Mathematics (1968–1980). From 1948 to 1980 he was the head of the topology section. One of his students was Andrzej Mostowski.

Legacy

Kazimierz Kuratowski was one of a celebrated group of Polish mathematicians who would meet at Lwów's Scottish Café. He was a president of the Polish Mathematical Society (PTM) and a member of the Warsaw Scientific Society (TNW). What is more, he was chief editor in "Fundamenta Mathematicae", a series of publications in "Polish Mathematical Society Annals". Furthermore, Kuratowski worked as an editor in the Polish Academy of Sciences Bulletin. He was also one of the writers of the Mathematical monographs, which were created in cooperation with the Institute of Mathematics of the Polish Academy of Sciences (IMPAN). High quality research monographs of the representatives of Warsaw's and Lwów's School of Mathematics, which concerned all areas of pure and applied mathematics, were published in these volumes.

Kazimierz Kuratowski was an active member of many scientific societies and foreign scientific academies, including the Royal Society of

Kazimierz Kuratowski Prize

In 1981, IMPAN, the Polish Mathematical Society, and Kuratowski's daughter Zofia Kuratowska established a prize in his name for achievements in mathematics to people under the age of 30 years.^[4] The prize is considered the most prestigious of awards for young Polish mathematicians; past recipients have included Józef H. Przytycki, Mariusz Lemańczyk, Tomasz Łuczak, Mikołaj Bojańczyk, and Wojciech Samotij.^[4]

Research

Kuratowski proved the Kuratowski-Zorn lemma (often called just Zorn's lemma) in 1922.^[5] This result has important connections to many basic theorems. Zorn gave its application in 1935.^[6] Kuratowski implemented many concepts in set theory and topology. In many cases, Kuratowski established new terminologies and symbolisms. His contributions to mathematics include:

• a characterization of topological spaces which are now called the 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 ${\displaystyle (x,y)}$ with the set ${\displaystyle \{\{x\},\{x,y\}\};}$^[7]
• the Kuratowski finite set definition, see
  Kuratowski-finite;^[8]
• introduction of the Tarski–Kuratowski algorithm;
• Kuratowski's closure-complement problem;
• Kuratowski's free set theorem;
• Kuratowski's intersection theorem;
• Knaster-Kuratowski fan
  ;
• Kuratowski-Ulam theorem
  ;
• Kuratowski convergence of subsets of metric spaces;
• the Kuratowski and Ryll-Nardzewski measurable selection theorem;

Kuratowski's post-war works were mainly focused on three strands:

• The development of homotopy in continuous functions.
• The construction of connected space theory in higher dimensions.
• The uniform depiction of cutting Euclidean spaces by any of its subsets, based on the properties of continuous transformations of these sets.

Publications

Among over 170 published works are valuable monographs and books including Topologie (Vol. I, 1933, translated into English and Russian, and Vol. II, 1950) and Introduction to Set Theory and Topology (Vol. I, 1952, translated into English, French, Spanish, and Bulgarian). He authored "A Half Century of Polish Mathematics 1920-1970: Remembrances and Reflections" (1973)

• Kuratowski, Kazimierz; Mostowski, Andrzej (1976) [1968], Set theory. With an introduction to descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 86 (Second ed.), Amsterdam-New York-Oxford: North-Holland Publishing Co.,
  MR 0485384

• List of Polish mathematicians
• Scottish Café
• Timeline of Polish science and technology

Notes

References