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Shape Theory (mathematics)
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. Background Shape theory was reinvented, further developed and promoted by the Polish mathematician Karol Borsuk in 1968. Actually, the name ''shape theory'' was coined by Borsuk. Warsaw Circle Borsuk lived and worked in Warsaw, hence the name of one of the fundamental examples of the area, the Warsaw circle. It is a compact subset of the plane produced by "closing up" a topologist's sine curve with an arc. The homotopy groups of the Warsaw circle are all trivial, just like those of a point, and so any map between the Warsaw circle and a point induces a weak homotopy equivalence. However these two spaces are not homotopy equivalent. So by the Whitehead theorem, the Wars ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Norman Steenrod
Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled ''Universal homology groups''. Steenrod held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He was editor of the Annals of Mathematics and a member of the National Academy of Sciences. He died in Princeton, survived by his wife, the former Carolyn Witter, and two children. Work Thanks to Lefschetz and others, the cup product structure of cohomology was understood by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Duke Mathematical Journal
''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz. Leonard Carlitz served on the editorial board for 35 years, from 1938 to 1973. The current managing editor is Richard Hain (Duke University). Impact According to the journal homepage, the journal has a 2018 impact factor of 2.194, ranking it in the top ten mathematics journals in the world. References External links * Mathematics journals Mathematical Journal In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in scientific journals are mostly written by active scientists such as s ... Publications established in 1935 Multilingual journals English-language journals French-lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lecture Notes In Mathematics
''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Springer Science+Business Media (formerly Springer-Verlag). The intent of the series is to publish not only lecture notes, but results from seminars and conferences, more quickly than the several-years-long process of publishing polished journal papers in mathematics. In order to speed the publication process, early volumes of the series (before electronic publishing) were reproduced photographically from typewritten manuscripts. According to Earl Taft it has been "enormously successful" and "is considered a very valuable service to the mathematical community". there have been 2232 volumes in this series. See also * ''Lecture Notes in Physics'' * ''Lecture Notes in Computer Science ''Lecture Notes in Computer Science'' is a series of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Rocky Mountain Journal Of Mathematics
''Rocky'' is a 1976 American sports drama film directed by John G. Avildsen and written by and starring Sylvester Stallone. It is the first installment in the ''Rocky'' franchise and stars Talia Shire, Burt Young, Carl Weathers, and Burgess Meredith. In the film, Rocky Balboa (Stallone), an uneducated, small-time club fighter and debt collector gets an unlikely shot at the world heavyweight championship held by Apollo Creed (Weathers). ''Rocky'' entered development in March 1975, after Stallone wrote the screenplay in three days. It entered a complicated production process after Stallone refused to allow the film to be made without him in the lead role; United Artists eventually agreed to cast Stallone after he rejected a six figure deal for the film rights. Principal photography began in January 1976, with filming primarily held in Philadelphia; several locations featured in the film, such as the Rocky Steps, are now considered cultural landmarks. With an estimated producti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mathematical Proceedings Of The Cambridge Philosophical Society
''Mathematical Proceedings of the Cambridge Philosophical Society'' is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society. It aims to publish original research papers from a wide range of pure and applied mathematics. The journal, formerly titled ''Proceedings of the Cambridge Philosophical Society'', has been published since 1843. See also *Cambridge Philosophical Society The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of l ... External linksofficial website Academic journals associated with learned and professional societies Cambridge University Press academic journals Mathematics education in the United Kingdom Mathematics journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Peter Hilton
Peter John Hilton (7 April 1923Peter Hilton, "On all Sorts of Automorphisms", '' The American Mathematical Monthly'', 92(9), November 1985, p. 6506 November 2010) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during World War II. Early life He was born in Brondesbury, London, the son Mortimer Jacob Hilton, a Jewish physician who was in general practice in Peckham, and his wife Elizabeth Amelia Freedman, and was brought up in Kilburn. The physiologist Sidney Montague Hilton (1921–2011) of the University of Birmingham Medical School was his elder brother. Hilton was educated at St Paul's School, London."About the speaker"announcement of a lecture given by Peter Hilton at Bletchley Park on 12 July 2006. Retrieved 18 January 2007. He went to The Queen's College, Oxford in 1940 to read mathematics, on an open scholarship, where the mathematics tutor was Ughtred Haslam-Jones. Bletchley Park A wartime undergraduate in wart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Simon & Schuster
Simon & Schuster () is an American publishing company and a subsidiary of Paramount Global. It was founded in New York City on January 2, 1924 by Richard L. Simon and M. Lincoln Schuster. As of 2016, Simon & Schuster was the third largest publisher in the United States, publishing 2,000 titles annually under 35 different imprints. History Early years In 1924, Richard Simon's aunt, a crossword puzzle enthusiast, asked whether there was a book of '' New York World'' crossword puzzles, which were very popular at the time. After discovering that none had been published, Simon and Max Schuster decided to launch a company to exploit the opportunity.Frederick Lewis Allen, ''Only Yesterday: An Informal History of the 1920s'', p. 165. . At the time, Simon was a piano salesman and Schuster was editor of an automotive trade magazine. They pooled , equivalent to $ today, to start a company that published crossword puzzles. The new publishing house used "fad" publishing to publish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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List Of Topologies
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property. Widely known topologies * The Baire space − \N^ with the product topology, where \N denotes the natural numbers endowed with the discrete topology. It is the space of all sequences of natural numbers. * Cantor set − A subset of the closed interval , 1/math> with remarkable properties. ** Cantor dust * Discrete topology − All subsets are open. * Euclidean topology − The natural topology on Euclidean space \Reals^n induced by the Euclidean metric, which is itself induced by the Euclidean norm. ** Real line − \Reals ** Space-filling curve ** Unit interval − , 1/math> * Extended real number line * Hilbert cube − , 1/1\times , 1/2\times , 1/3\times \cdots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Operator Algebra
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of operator algebras are phrased in algebraic terms, while the techniques used are highly analytic.''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi Although the study of operator algebras is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Overview Operator algebras can be used to study arbitrary sets of operators with little algebraic relation ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general operator algebras are non-commutative rings. An operator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |