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Roman Sikorski
Roman Sikorski (July 11, 1920 – September 12, 1983) was a Polish mathematician. Biography Sikorski was a professor at the University of Warsaw from 1952 until 1982. Since 1962, he was a member of the Polish Academy of Sciences. Sikorski's research interests included: Boolean algebras, mathematical logic, functional analysis, the theory of distributions, measure theory, general topology, and descriptive set theory. Works * ''Boolean Algebras'' (1960) * ''Funkcje rzeczywiste'' (t. 1–2 1958–59) * ''The Mathematics of Metamathematics'' (1963, together with Helena Rasiowa) * ''Rachunek rózniczkowy i całkowy — funkcje wielu zmiennych'' (1967) See also * 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 pu ... References * Roman Sikorsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mszczonów
Mszczonów (Yiddish: אַמשינאָוו ''Amshinov'') is a town in Żyrardów County, Masovian Voivodeship, Poland, with 6,231 inhabitants as of the 2006 census. It is situated just outside the Warsaw metropolitan area, approximately 45 km from Warsaw city centre. History The oldest known mention of Mszczonów comes from a document of Duke Konrad I of Masovia from 1245, when it was part of fragmented Piast-ruled Poland. Mszczonów was granted town rights in 1377 or earlier. It was a royal town of Poland, administratively located in the Rawa Voivodeship in the Greater Poland Province. One of two main routes connecting Warsaw and Dresden ran through the town in the 18th century and Kings Augustus II the Strong and Augustus III of Poland often traveled that route. The town possessed a vibrant Jewish community, and it was once the center of the Hasidic Amshinov dynasty (Mszczonów being pronounced as "Amshinov" in Yiddish.) During the invasion of Poland, which started Wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1920 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slip ... [...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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helena Rasiowa
Helena Rasiowa (20 June 1917 – 9 August 1994) was a Polish mathematician. She worked in the foundations of mathematics and algebraic logic. Early years Rasiowa was born in Vienna on 20 June 1917 to Polish parents. As soon as Poland regained its independence in 1918, the family settled in Warsaw. Helena's father was a railway specialist. She exhibited many different skills and interests, from music to business management and the most important of her interests, mathematics. In 1938, the time was not very opportune for entering a university. Rasiowa had to interrupt her studies, as no legal education was possible in Poland after 1939. Many people fled the country, or at least they fled the big towns, which were subject to German bombardment and terror. The Rasiowa family fled also, as most high-ranking administration officials and members of the government were being evacuated to Romania. The family spent a year in Lviv. After the Soviet invasion in September 1939, the town ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descriptive Set Theory
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the study of operator algebras and group actions, and mathematical logic. Polish spaces Descriptive set theory begins with the study of Polish spaces and their Borel sets. A Polish space is a second-countable topological space that is metrizable with a complete metric. Heuristically, it is a complete separable metric space whose metric has been "forgotten". Examples include the real line \mathbb, the Baire space \mathcal, the Cantor space \mathcal, and the Hilbert cube I^. Universality properties The class of Polish spaces has several universality properties, which show that there is no loss of generality in considering Polish spaces of certain restricted form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. The fundamental concepts in point-set topology are ''continuity'', ''compactness'', and ''connectedness'': * Continuous functions, intuitively, take nearby points to nearby points. * Compact sets are those that can be covered by finitely many sets of arbitrarily small size. * Connected sets are sets that cannot be divided into two pieces that are far apart. The terms 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using the concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a ''t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution (mathematics)
Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions than classical solutions, or where appropriate classical solutions may not exist. Distributions are also important in physics and engineering where many problems naturally lead to differential equations whose solutions or initial conditions are singular, such as the Dirac delta function. A function f is normally thought of as on the in the function domain by "sending" a point x in its domain to the point f(x). Instead of acting on points, distribution theory reinterpr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grodzisk Mazowiecki
Grodzisk Mazowiecki is a town in central Poland with 29,363 inhabitants (2011). It is 30 km. southwest of Warsaw. Between 1975 and 1998 it was situated in the Warszawa Voivodeship but since 1999 it has been situated in the Masovian Voivodeship. It is the capital of Grodzisk Mazowiecki County. Demography ImageSize = width:400 height:300 PlotArea = left:70 right:40 top:20 bottom:20 TimeAxis = orientation:vertical AlignBars = justify Colors = id:gray1 value:gray(0.9) DateFormat = yyyy Period = from:0 till:35000 ScaleMajor = unit:year increment:10000 start:0 gridcolor:gray1 PlotData = bar:1995 color:gray1 width:1 from:0 till:24962 width:15 text:24962 textcolor:red fontsize:8px bar:1997 color:gray1 width:1 from:0 till:25202 width:15 text:25202 textcolor:red fontsize:8px bar:2000 color:gray1 width:1 from:0 till:25397 width:15 text:25397 textcolor:red fontsize:8px bar:2002 color:gray1 width:1 from:0 till:26005 width:15 text:26005 textcolor:red fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution). Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle. __TOC__ History The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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