In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,
Wacław Franciszek Sierpiński was a Polish mathematician. He was known for contributions to set theory, number theory, theory of functions, and topology. He published over 700 papers and 50 books.
Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. He worked as a professor at the University of Warsaw and at the Mathematical Institute of the Polish Academy of Sciences. Between 1946 and 1953, he served as President of the Polish Mathematical Society.
Hugo Dyonizy Steinhaus was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Zygmunt Janiszewski was a Polish mathematician.
Antoni Zygmund was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.
Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They published in the journal Fundamenta Mathematicae, founded in 1920—one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski—whose illustrious career would a few years later take him to the University of California, Berkeley—published his celebrated theorem on the undefinability of the notion of truth.
Andrzej Mostowski was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma.
The Polish Mathematical Society is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU).
The Polish School of Mathematics was the mathematics community that flourished in Poland in the 20th century, particularly during the Interbellum between World Wars I and II.
Andrzej Ehrenfeucht is a Polish-American mathematician and computer scientist.
In topology, a branch of mathematics, the Knaster–Kuratowski fan is a specific connected topological space with the property that the removal of a single point makes it totally disconnected. It is also known as Cantor's leaky tent or Cantor's teepee, depending on the presence or absence of the apex.
Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory.
Indagationes Mathematicae is a Dutch mathematics journal.
Topology and Its Applications is a peer-reviewed mathematics journal publishing research on topology. It was established in 1971 as General Topology and Its Applications, and renamed to its current title in 1980. The journal currently publishes 18 issues each year in one volume. It is indexed by Scopus, Mathematical Reviews, and Zentralblatt MATH. Its 2004–2008 MCQ was 0.38 and its 2020 impact factor was 0.617.
In mathematics, the Kuratowski–Ulam theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam, called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces.
Wanda Szmielew née Montlak was a Polish mathematical logician who first proved the decidability of the first-order theory of abelian groups.
Mathematica Applicanda is a peer-reviewed scientific journal covering applied mathematics. It was established in 1973 by the Polish Mathematical Society as Series III of the Annales Societatis Mathematicae Polonae, under the name Matematyka Stosowana. The first editor-in-chief was Marceli Stark. In 1999 the journal was renamed Matematyka Stosowana-Matematyka dla Społeczeństwa. Since 2012 its main issue is the electronic one with the name Mathematica Applicanda with ISSN 2299-4009.
Probability and Mathematical Statistics is a peer-reviewed scientific journal covering mathematical aspects of the probability theory. It was founded in 1980 as the initiative of the Wrocław probability community led by Kazimierz Urbanik and Czesław Ryll-Nardzewski, and statistics community represented by Witold Klonecki. They served as editors of the journal during the first twenty-five years of its existence, with Kazimierz Urbanik shouldering the role of the editor-in-chief. Beginning with 2007, Probability and Mathematical Statistics became an affiliated journal of the Institute of Mathematical Statistics. PMS is indexed by Scopus, MathSciNet, Index Copernicus and Journal Citation Reports (IF=0.617). PMS is an open-access journal.
In mathematics, Kuratowski's intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection. Kuratowski's result is a generalisation of Cantor's intersection theorem. Whereas Cantor's result requires that the sets involved be compact, Kuratowski's result allows them to be non-compact, but insists that their non-compactness "tends to zero" in an appropriate sense. The theorem is named for the Polish mathematician Kazimierz Kuratowski, who proved it in 1930.
