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Bronisław Knaster
Bronisław Knaster (22 May 1893 – 3 November 1980) was a Polish mathematician; from 1939 a university professor in Lwów and from 1945 in Wrocław. He is known for his work in point-set topology and in particular for his discoveries in 1922 of the hereditarily indecomposable continuum or pseudo-arc and of the Knaster continuum, or buckethandle continuum. Together with his teacher Hugo Steinhaus and his colleague Stefan Banach, he also developed the last diminisher procedure for fair cake cutting. Knaster received his Ph.D. degree from University of Warsaw in 1925, under the supervision of Stefan Mazurkiewicz. See also * Knaster–Tarski theorem *Knaster–Kuratowski fan *Knaster's condition In mathematics, a partially ordered set ''P'' is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset ''A'' of ''P'' has an upwards-linked uncountable subset. An analogous definition applies to Knaster's con ... References 1893 births 199 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officially estimated at 1.86 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 7th most-populous city in the European Union. The city area measures and comprises 18 districts, while the metropolitan area covers . Warsaw is an Alpha global city, a major cultural, political and economic hub, and the country's seat of government. Warsaw traces its origins to a small fishing town in Masovia. The city rose to prominence in the late 16th century, when Sigismund III decided to move the Polish capital and his royal court from Kraków. Warsaw served as the de facto capital of the Polish–Lithuanian Commonwealth until 1795, and subsequently as the seat of Napoleon's Duchy of Warsaw. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugo Steinhaus
Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) 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 (now Lviv, Ukraine), 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. Author of around 170 scientific articles and books, Steinhaus has left his legacy and contribution in many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the earl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw School Of Mathematics
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. Notable members of the Warsaw School of Mathematics have included: * Wacław Sierpiński * Kazimierz Kuratowski * Edward Marczewski * Bronisław Knaster * Zygmunt Janiszewski * Stefan Mazurkiewicz * Stanisław Saks * Karol Borsuk * Roman Sikorski * Nachman Aronszajn * Samuel Eilenberg Additionally, notable logicians of the Lwów–Warsaw School of Logic, working at Warsaw, have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic Church monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word ''universitas'' (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Warsaw Governorate
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1990 Deaths
Year 199 ( CXCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was sometimes known as year 952 ''Ab urbe condita''. The denomination 199 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Mesopotamia is partitioned into two Roman provinces divided by the Euphrates, Mesopotamia and Osroene. * Emperor Septimius Severus lays siege to the city-state Hatra in Central-Mesopotamia, but fails to capture the city despite breaching the walls. * Two new legions, I Parthica and III Parthica, are formed as a permanent garrison. China * Battle of Yijing: Chinese warlord Yuan Shao defeats Gongsun Zan. Korea * Geodeung succeeds Suro of Geumgwan Gaya, as king of the Korean kingdom of Gaya (traditional date). By topic Religion * Pope Zephyrinus succeeds Pope Vic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1893 Births
Events January–March * January 2 – Webb C. Ball introduces railroad chronometers, which become the general railroad timepiece standards in North America. * Mark Twain started writing Puddn'head Wilson. * January 6 – The Washington National Cathedral is chartered by Congress; the charter is signed by President Benjamin Harrison. * January 13 ** The Independent Labour Party of the United Kingdom has its first meeting. ** U.S. Marines from the ''USS Boston'' land in Honolulu, Hawaii, to prevent the queen from abrogating the Bayonet Constitution. * January 15 – The ''Telefon Hírmondó'' service starts with around 60 subscribers, in Budapest. * January 17 – Overthrow of the Kingdom of Hawaii: Lorrin A. Thurston and the Committee of Safety (Hawaii), Citizen's Committee of Public Safety in Hawaii, with the intervention of the United States Marine Corps, overthrow the government of Queen Liliuokalani. * January 21 ** The Cherry Sisters first perform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knaster's Condition
In mathematics, a partially ordered set ''P'' is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset ''A'' of ''P'' has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Knaster's condition implies the countable chain condition (ccc), and it is sometimes used in conjunction with a weaker form of Martin's axiom, where the ccc requirement is replaced with Knaster's condition. Not unlike ccc, Knaster's condition is also sometimes used as a property of a topological space, in which case it means that the topology (as in, the family of all open sets) with inclusion Inclusion or Include may refer to: Sociology * Social inclusion, aims to create an environment that supports equal opportunity for individuals and groups that form a society. ** Inclusion (disability rights), promotion of people with disabilitie ... satisfies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knaster–Kuratowski Fan
In topology, a branch of mathematics, the Knaster–Kuratowski fan (named after Polish mathematicians Bronisław Knaster and Kazimierz Kuratowski) 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 (after Georg Cantor), depending on the presence or absence of the apex. Let C be the Cantor set In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883. T ..., let p be the point \left(\tfrac1,\tfrac1\right)\in\mathbb R^2, and let L(c), for c \in C, denote the line segment connecting (c,0) to p. If c \in C is an endpoint of an interval deleted in the Cantor set, let X_ = \; for all other points in C let X_ = \; the Knaster–Kuratowski fan is defined as \bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knaster–Tarski Theorem
In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following: :''Let'' (''L'', ≤) ''be a complete lattice and let f : L → L be an monotonic function (w.r.t. ≤ ). Then the set of fixed points of f in L also forms a complete lattice under ≤ .'' It was Tarski who stated the result in its most general form, and so the theorem is often known as Tarski's fixed-point theorem. Some time earlier, Knaster and Tarski established the result for the special case where ''L'' is the lattice of subsets of a set, the power set lattice. The theorem has important applications in formal semantics of programming languages and abstract interpretation. A kind of converse of this theorem was proved by Anne C. Davis: If every order preserving function ''f'' : ''L'' → ''L'' on a lattice ''L'' has a fixed point, then ''L'' is a complete lattice. Consequences: least and greatest fixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw
The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of study as well as 100 specializations in humanities, technical, and the natural sciences. The University of Warsaw consists of 126 buildings and educational complexes with over 18 faculties: biology, chemistry, journalism and political science, philosophy and sociology, physics, geography and regional studies, geology, history, applied linguistics and philology, Polish language, pedagogy, economics, law and public administration, psychology, applied social sciences, management and mathematics, computer science and mechanics. The University of Warsaw is one of the top Polish universities. It was ranked by '' Perspektywy'' magazine as best Polish university in 2010, 2011, 2014, and 2016. International rankings such as ARWU and Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Cake Cutting
Fair cake-cutting is a kind of fair division problem. The problem involves a ''heterogeneous'' resource, such as a cake with different toppings, that is assumed to be ''divisible'' – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be ''unanimously'' fair - each person should receive a piece that he or she believes to be a fair share. The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. The prototypical procedure for fair cake-cutting is divide and choose, which is mentioned already in the book of Genesis. It solves the fair division problem for two people. The moder ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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