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Leopold Vietoris
Leopold Vietoris (; ; 4 June 1891 – 9 April 2002) was an Austrian mathematician, World War I veteran and supercentenarian. He was born in Radkersburg and died in Innsbruck. He was known for his contributions to topology—notably the Mayer–Vietoris sequence—and other fields of mathematics, his interest in history of mathematics, mathematical history and for being a keen alpinist. Biography Vietoris studied mathematics and geometry at the TU Wien, Vienna University of Technology. He was drafted in 1914 in World War I and was wounded in September that same year. On 4 November 1918, one week before the Armistice of Villa Giusti, he became an Italy, Italian prisoner of war. After returning to Austria, he attended the University of Vienna, where he earned his PhD in 1920, with a thesis written under the supervision of Gustav von Escherich and Wilhelm Wirtinger. In autumn 1928 he married his first wife Klara Riccabona, who later died while giving birth to their sixth daughter. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bad Radkersburg
Bad Radkersburg (; sl, Radgona; archaic hu, RegedeDivald, Kornél. 1931. ''Old Hungarian Art''. London: Oxford University Press, p. 117.) is a spa town in the southeast of the Austrian States of Austria, state of Styria, in the Districts of Austria, district of Südoststeiermark District, Südoststeiermark. Geography In the south the town borders Slovenia on the Mur (river), Mur River. On the other side of the river lies its Twin cities (geographical proximity), twin city Gornja Radgona (''Oberradkersburg'') in the Styria (Slovenia), Slovenian Styria region. Bad Radkersburg is a spa town featuring a thermal spring with a temperature of . This and the longest sunshine duration in Austria make it an attractive site for tourism with over 100,000 stays per year. In the course of a Styrian administrative reform, the town merged with the neighbouring municipality of Radkersburg Umgebung with combined population of 3158 inhabitants, in effect from 1 January 2015. Weather Histor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mayer–Vietoris Sequence
In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to two Austrian mathematicians, Walther Mayer and Leopold Vietoris. The method consists of splitting a space into subspaces, for which the homology or cohomology groups may be easier to compute. The sequence relates the (co)homology groups of the space to the (co)homology groups of the subspaces. It is a natural long exact sequence, whose entries are the (co)homology groups of the whole space, the direct sum of the (co)homology groups of the subspaces, and the (co)homology groups of the intersection of the subspaces. The Mayer–Vietoris sequence holds for a variety of cohomology and homology theories, including simplicial homology and singular cohomology. In general, the sequence holds for those theories satisfying the Eilenberg–Steenr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vietoris–Rips Complex
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is a way of forming a topological space from distances in a set of points. It is an abstract simplicial complex that can be defined from any metric space ''M'' and distance δ by forming a simplex for every finite set of points that has diameter at most δ. That is, it is a family of finite subsets of ''M'', in which we think of a subset of ''k'' points as forming a (''k'' − 1)-dimensional simplex (an edge for two points, a triangle for three points, a tetrahedron for four points, etc.); if a finite set ''S'' has the property that the distance between every pair of points in ''S'' is at most δ, then we include ''S'' as a simplex in the complex. History The Vietoris–Rips complex was originally called the Vietoris complex, for Leopold Vietoris, who introduced it as a means of extending homology theory from simplicial complexes to metric spaces. After Eliyahu Rips applie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vietoris–Begle Mapping Theorem
The Vietoris–Begle mapping theorem is a result in the mathematics, mathematical field of algebraic topology. It is named for Leopold Vietoris and Edward G. Begle. The statement of the theorem, below, is as formulated by Stephen Smale. Theorem Let X and Y be compact space, compact metric spaces, and let f:X\to Y be surjective function, surjective and continuous function, continuous. Suppose that the image (mathematics), fibers of f are acyclic complex, acyclic, so that :\tilde H_r(f^(y)) = 0, for all 0\leq r\leq n-1 and all y\in Y, with \tilde H_r denoting the rth reduced homology, reduced Vietoris homology group (mathematics), group. Then, the induced homomorphism :f_*:\tilde H_r(X)\to\tilde H_r(Y) is an isomorphism for r\leq n-1 and a surjection for r=n. Note that as stated the theorem doesn't hold for homology theories like singular homology. For example, Vietoris homology groups of the closed topologist's sine curve and of a segment are isomorphic (since the first projects ont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homology Theory
In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry. The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry. The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Von Escherich
Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician. Biography Born in Mantua, he studied mathematics and physics at the University of Vienna. From 1876 to 1879 he was professor at the University of Graz. In 1882 he went to the Graz University of Technology and in 1884 he went to the University of Vienna, where he also was president of the university in 1903/04. Together with Emil Weyr he founded the journal '' Monatshefte für Mathematik und Physik'' and together with Ludwig Boltzmann and Emil Müller he founded the Austrian Mathematical Society. Escherich died in Vienna. Work on hyperbolic geometry Following Eugenio Beltrami's (1868) discussion of hyperbolic geometry, Escherich in 1874 published a paper named "The geometry on surfaces of constant negative curvature". He used coordinates initially introduced by Christoph Gudermann (1830) for spherical geometry, which were adapted by Escherich using hyperbolic functions. For the case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prisoner Of War
A prisoner of war (POW) is a person who is held captive by a belligerent power during or immediately after an armed conflict. The earliest recorded usage of the phrase "prisoner of war" dates back to 1610. Belligerents hold prisoners of war in custody for a range of legitimate and illegitimate reasons, such as isolating them from the enemy combatants still in the field (releasing and repatriating them in an orderly manner after hostilities), demonstrating military victory, punishing them, prosecuting them for war crimes, exploiting them for their labour, recruiting or even conscripting them as their own combatants, collecting military and political intelligence from them, or indoctrinating them in new political or religious beliefs. Ancient times For most of human history, depending on the culture of the victors, enemy fighters on the losing side in a battle who had surrendered and been taken as prisoners of war could expect to be either slaughtered or enslaved. Ear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical region. Italy is also considered part of Western Europe, and shares land borders with France, Switzerland, Austria, Slovenia and the enclaved microstates of Vatican City and San Marino. It has a territorial exclave in Switzerland, Campione. Italy covers an area of , with a population of over 60 million. It is the third-most populous member state of the European Union, the sixth-most populous country in Europe, and the tenth-largest country in the continent by land area. Italy's capital and largest city is Rome. Italy was the native place of many civilizations such as the Italic peoples and the Etruscans, while due to its central geographic location in Southern Europe and the Mediterranean, the country has also historically been home ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armistice Of Villa Giusti
The Armistice of Villa Giusti or Padua ended warfare between Italy and Austria-Hungary on the Italian Front during World War I. The armistice was signed on 3 November 1918 in the Villa Giusti, outside Padua in the Veneto, Northern Italy, and took effect 24 hours later. Background By the end of October 1918, the Austro-Hungarian Army was so fatigued that its commanders were forced to seek a ceasefire. By 1918 the Austro-Hungarian Empire was tearing itself apart under ethnic lines, and if the Dual Monarchy were to survive, it needed to withdraw from the war. In the final stage of the Battle of Vittorio Veneto, a stalemate was reached, and the troops of Austria-Hungary started a chaotic withdrawal. On 28 October, Austria-Hungary began to negotiate a truce but hesitated to sign the text of the armistice. In the meantime, the Italians reached Trento and Udine, and landed in Trieste. After a threat to break off negotiations, the Austro-Hungarians, on 3 November, accepted the armisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
