KURATOWSKI TOPOLOGIA PDF

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Kazimierz Kuratowski Polish pronunciation: He was one of the leading representatives of the Warsaw School of Mathematics.

Kazimierz Kuratowski was born in WarsawVistula Land the part of the former Kingdom of Poland controlled by the Russian Empireon 2 Februaryinto an assimilated Jewish family. Inhe enrolled in an engineering course at the University of Glasgow in Scotlandin part because he did not wish to study in Russian; instruction in Polish was prohibited. He completed only one year of study when the outbreak of World War I precluded any further enrollment.

InRussian forces withdrew iuratowski Warsaw and Warsaw University was reopened with Polish as the language of topolgia. Kuratowski restarted his university education there the same year, this time in mathematics.

Kuratowski’s theorem

He obtained his Ph. In autumn Kuratowski was awarded the Ph. His thesis statement consisted of two parts. One was devoted to kuratiwski axiomatic construction of topology via the closure axioms. This first part republished in a slightly modified form in has been cited in hundreds of scientific articles.

The second part of Kuratowski’s thesis was devoted to continua irreducible between two points. This was the subject of a French doctoral thesis written by Zygmunt Janiszewski. Two years later, inKuratowski was appointed deputy professor of mathematics at Warsaw University.

He was the head of the Mathematics department there until Kuratowski was also dean of the department twice. InKuratowski became a member of the Warsaw Scientific Society. He did however, collaborate closely with Banach in solving important problems in measure theory. In he was appointed the professor at Warsaw University.

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A year later Kuratowski was nominated as the head of Mathematics Department there. During World War II, he gave lectures yopologia the underground university in Warsawsince higher education for Poles was forbidden under German occupation. In FebruaryKuratowski started to lecture at the reopened Warsaw University.

Topologie 1: Espaces Metrisables, Espaces Complets: C Kuratowski: : Books

Inhe became a member of the Polish Academy of Learningin he was appointed vice-president of the Mathematics department at Warsaw University, and from he was chosen to be the vice-president of Warsaw Scientific Society. In he became a member of the Polish Academy of Sciencesof kuuratowski he was the vice-president from to He helped to establish the State Mathematical Institute, which was incorporated into the Polish Academy of Sciences in From until 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.

From to he was the head of the topology section. One of his students was Andrzej Mostowski. What topologoa more, he was chief editor in “Fundamenta Mathematicae”, a series of publications in “Polish Mathematical Society Annals”. He implemented the closure axioms known in mathematical circles as the Kuratowski closure axioms. This was fundamental for the development of topological space theory and irreducible continuum theory between two points.

The most valuable results, which were obtained by Kazimierz Kuratowski after the war are those that concern the relationship between topology and analytic functions theoryand also research in the field of cutting Euclidean spaces.

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Knaster and Kuratowski brought a comprehensive and precise study to connected components theory. It was applied to issues such as cutting-plane, with the paradoxical examples of connected components.

Kuratowski proved the Kuratowski-Zorn lemma often called just Zorn’s lemma in Zorn gave its application in In many cases, Kuratowski established new terminology and symbolism.

Kazimierz Kuratowski

His contributions to mathematics include:. Among over published works are valuable monographs and books including Topologie Vol. I,translated into English and Russian, and Vol. I,translated into English, French, Spanish, and Bulgarian.

Kazimierz Kuratowski – Wikipedia

Remembrances and Reflections” [9] and “Notes to his autobiography” The latter was published posthumously thanks to Kuratowski’s daughter Zofia Kuratowska, who prepared his notes for printing.

Kazimierz Kuratowski represented Polish mathematics in the International Mathematics Union where he was vice president from to What is more, he participated in numerous international congresses and lectured at dozens of universities around the world.

He received the highest national awards, as well as a gold medal of the Czechoslovak Academy of Sciencesand the Polish Academy of Science. Kuratowski died on 18 June in Warsaw. From Wikipedia, the free encyclopedia.

Stefan Mazurkiewicz Zygmunt Janiszewski. Retrieved 19 July Kazimierz Kuratowski in Topology”. Polish Academy of Sciences. A Half Century of Polish Mathematics: Retrieved from ” https: Views Read Edit View history. In other projects Wikimedia Commons. This page was last edited on 17 Octoberat By using this site, you agree to the Terms of Use and Privacy Policy.