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Georg Nöbeling
Georg August Nöbeling (12 November 1907 – 16 February 2008) was a German mathematician. Education and career Born and raised in Lüdenscheid, Nöbeling studied mathematics and physics at University of Göttingen between 1927 and 1929 and University of Vienna, where he was a student of Karl Menger and received his PhD in 1931 on a generalization of the embedding theorem, which for one special case can be visualized by the Menger sponge. Nöbeling worked and researched in Menger's Mathematical Colloquium with Kurt Gödel, Franz Alt, Abraham Wald, Olga Taussky-Todd and others. In 1933, he moved to the University of Erlangen, where he habilitated in 1935 under Otto Haupt and obtained a professorship at the same place in 1940. His work focused on analysis, topology, and geometry. 1968/1969 he solved Specker's theorem on abelian groups. As Rector (1962–1963) of the University of Erlangen he oversaw the merge with the business college in Nuremberg. He also served twice as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lüdenscheid
Lüdenscheid () is a city in the Märkischer Kreis district, in North Rhine-Westphalia, Germany. It is located in the Sauerland region. Geography Lüdenscheid is located on the saddle of the watershed between the Lenne and Volme rivers which both empty into the Ruhr river (which subsequently flows into the Rhine), with three smaller valleys leading to them. The saddle has a height of 420 meters, higher elevations on the watershed are an unnamed hilltop of 505 meters in the north, and the 663 meters high ''Nordhelle'' in the Ebbe Mountains range. In the surrounding mountainous area, six dams created reservoirs to regulate the water flow in the Ruhr river and supply drinking water. The mountainous nature of the city's territory gave rise to the nickname "Bergstadt" (mountain town). The original settlement circles around the church built on a ledge of the slope above the saddle. Climate History While first settlement in the Lüdenscheid area is confirmed for the 9th cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Wald
Abraham Wald (; ; , ; – ) was a Hungarian and American mathematician and statistician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations. He spent his research career at Columbia University. He was the grandson of Rabbi Moshe Shmuel Glasner. Life and career Wald was born on 31 October 1902 in Cluj-Napoca, Kolozsvár, Transylvania, in the Kingdom of Hungary. A religious Jew, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was homeschooled by his parents until college. His parents were quite knowledgeable and competent as teachers. In 1928, he graduated in mathematics from the Babeș-Bolyai University, King Ferdinand I University. In 1927, he had entered Postgraduate education, g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Space
In mathematics, a universal space is a certain metric space that contains all metric spaces whose dimension is bounded by some fixed constant. A similar definition exists in topological dynamics. Definition Given a class \textstyle \mathcal of topological spaces, \textstyle \mathbb\in\mathcal is universal for \textstyle \mathcal if each member of \textstyle \mathcal embeds in \textstyle \mathbb. Menger stated and proved the case \textstyle d=1 of the following theorem. The theorem in full generality was proven by Nöbeling. Theorem: The \textstyle (2d+1)-dimensional cube \textstyle ,1 is universal for the class of compact metric spaces whose Lebesgue covering dimension is less than \textstyle d. Nöbeling went further and proved: Theorem: The subspace of \textstyle ,1 consisting of set of points, at most \textstyle d of whose coordinates are rational, is universal for the class of separable metric spaces whose Lebesgue covering dimension is less than \textstyle d. The last ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Dimension
In the mathematical field of topology, the inductive dimension of a topological space ''X'' is either of two values, the small inductive dimension ind(''X'') or the large inductive dimension Ind(''X''). These are based on the observation that, in ''n''-dimensional Euclidean space ''R''''n'', (''n'' − 1)-dimensional spheres (that is, the boundaries of ''n''-dimensional balls) have dimension ''n'' − 1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets. The small and large inductive dimensions are two of the three most usual ways of capturing the notion of "dimension" for a topological space, in a way that depends only on the topology (and not, say, on the properties of a metric space). The other is the Lebesgue covering dimension. The term "topological dimension" is ordinarily understood to refer to the Lebesgue covering dimension. For "sufficiently nice" s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bavarian Academy Of Sciences And Humanities
The Bavarian Academy of Sciences and Humanities () is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledge within their subject. The general goal of the academy is the promotion of interdisciplinary encounters and contacts and the cooperation of representatives of different subjects. History On 12 October 1758 the lawyer Johann Georg von Lori (1723–1787), Privy Counsellor at the College of Coinage and Mining in Munich, founded the ''Bayerische Gelehrte Gesellschaft'' (Learned Society of Bavaria). This led to the foundation by Maximilian III Joseph, Elector of Bavaria, of the Bavarian Academy of Sciences and Humanities on 28 March 1759. Count Sigmund von Haimhausen was the first president. The Academy's foundation charter specifically mentions the Parnassus Boicus, an earlier learned society. Originally, the Academy consisted of two divisions, the Class for History (''Historische Kla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Mathematical Society
The German Mathematical Society (, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in 1890 in Bremen with the set theorist Georg Cantor as first president. Founding members included Georg Cantor, Felix Klein, Walther von Dyck, David Hilbert, Hermann Minkowski, Carl Runge, Rudolf Sturm, Hermann Schubert, and Heinrich Weber. The current president of the DMV is . Activities In honour of its founding president, Georg Cantor, the society awards the Cantor Medal. The DMV publishes two scientific journals, the ''Jahresbericht der DMV'' and ''Documenta Mathematica''. It also publishes a quarterly magazine for its membership the ''Mitteilungen der DMV''. The annual meeting of the DMV is called the ''Jahrestagung''; the DMV traditionally meets every four years together with the Austrian Mathematical Society (ÖMG) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuremberg
Nuremberg (, ; ; in the local East Franconian dialect: ''Nämberch'' ) is the Franconia#Towns and cities, largest city in Franconia, the List of cities in Bavaria by population, second-largest city in the States of Germany, German state of Bavaria, and its 544,414 (2023) inhabitants make it the List of cities in Germany by population, 14th-largest city in Germany. Nuremberg sits on the Pegnitz (river), Pegnitz, which carries the name Regnitz from its confluence with the Rednitz in Fürth onwards (), and on the Rhine–Main–Danube Canal, that connects the North Sea to the Black Sea. Lying in the Bavarian Regierungsbezirk, administrative region of Middle Franconia, it is the largest city and unofficial capital of the entire cultural region of Franconia. The city is surrounded on three sides by the , a large forest, and in the north lies (''garlic land''), an extensive vegetable growing area and cultural landscape. The city forms a continuous conurbation with the neighbouring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rector (academia)
A rector (Latin language, Latin for 'ruler') is a senior official in an educational institution, and can refer to an official in either a university or a secondary school. Outside the English-speaking world, the rector is often the most senior official in a university, while in the United States, the equivalent is often referred to as the President (education), president, and in the United Kingdom and Commonwealth of Nations, the equivalent is the Vice-chancellor (education), vice-chancellor. The term and office of a rector can be referred to as a rectorate. The title is used widely in universities in EuropeEuropean nations where the word ''rector'' or a cognate thereof (''rektor'', ''recteur'', etc.) is used in referring to university administrators include Albania, Austria, Benelux, the Benelux, Bosnia and Herzegovina, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Germany, Greece, Hungary, Iceland, Italy, Latvia, Malta, Moldova, North Macedonia, Poland, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after the Norwegian mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation ･ , that combines any two elements a and b of A to form another element of A, denoted a \cdot b. The sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Specker
Ernst Paul Specker (11 February 1920, Zürich – 10 December 2011, Zürich) was a Swiss mathematician. Much of his most influential work was on Quine's New Foundations, a set theory with a universal set, but he is most famous for the Kochen–Specker theorem in quantum mechanics, showing that certain types of hidden-variable theories are impossible. He also proved the ordinal partition relation thereby solving a problem of Erdős. Specker received his Ph.D. in 1949 from ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...,. where he remained throughout his professional career. See also * Specker sequence * Baer–Specker group References External links Biography at the University of St. Andrews Ernst Specker (1920-2011) Martin Fürer, January 25, 2012. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
