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Raymond Wilder
Raymond Louis Wilder (3 November 1896 in Palmer, Massachusetts – 7 July 1982 in Santa Barbara, California) was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests. Life Wilder's father was a printer. Raymond was musically inclined. He played cornet in the family orchestra, which performed at dances and fairs, and accompanied silent films on the piano. He entered Brown University in 1914, intending to become an actuary. During World War I, he served in the U.S. Navy as an ensign. Brown awarded him his first degree in 1920, and a master's degree in actuarial mathematics in 1921. That year, he married Una Maude Greene; they had four children, thanks to whom they have ample descent. Wilder chose to do his Ph.D. at the University of Texas at Austin, the most fateful decision of his life. At Texas, Wilder discovered pure mathematics and topology, thanks to the remarkable influence of Robert Lee Moore, the founder ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palmer, Massachusetts
Palmer is a city in Hampden County, Massachusetts, United States. The population was 12,448 at the 2020 census. It is part of the Springfield, Massachusetts Metropolitan Statistical Area. Palmer adopted a home rule charter in 2004 with a council-manager form of government. Palmer is one of thirteen Massachusetts municipalities that have city forms of government but retain "The town of" in their official names. The villages of Bondsville, Thorndike, Depot Village, and Three Rivers are located in Palmer. History Palmer is composed of four separate and distinct villages: Depot Village, typically referred to simply as "Palmer" (named for the ornate Union Station railroad terminal designed by architect Henry Hobson Richardson), Thorndike, Three Rivers, and Bondsville. The villages began to develop their distinctive characters in the 18th century, and by the 19th century two rail lines and a trolley line opened the town to population growth. Today, each village has its own pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California At Santa Barbara
The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a public land-grant research university in Santa Barbara, California with 23,196 undergraduates and 2,983 graduate students enrolled in 2021–2022. It is part of the University of California 10-university system. Tracing its roots back to 1891 as an independent teachers' college, UCSB joined the University of California system in 1944, and is the third-oldest undergraduate campus in the system, after UC Berkeley and UCLA. Located on a WWII-era Marine air station, UC Santa Barbara is organized into three undergraduate colleges ( College of Letters and Science, College of Engineering, College of Creative Studies) and two graduate schools (Gevirtz Graduate School of Education and Bren School of Environmental Science & Management), offering more than 200 degrees and programs. The university has 10 national research centers, including the Kavli Institute for Theoretical Physics and the Center for Control, Dy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set-theoretic Topology
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independence (mathematical logic), independent of Zermelo–Fraenkel set theory (ZFC). Objects studied in set-theoretic topology Dowker spaces In the mathematics, mathematical field of general topology, a Dowker space is a topological space that is normal space, T4 but not paracompact space, countably paracompact. Clifford Hugh Dowker, Dowker conjectured that there were no Dowker spaces, and the conjecture was not resolved until Mary Ellen Rudin, M.E. Rudin constructed one in 1971. Rudin's counterexample is a very large space (of cardinality \aleph_\omega^) and is generally not well-behaved. Zoltán Tibor Balogh, Zoltán Balogh gave the first ZFC construction of a small (cardinality Cardinality of the continuum, continuum) example, which was more well-behaved than Rudin's. Using PCF theory, M. Kojman and Saharon Shelah, S. Shelah const ... [...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] |
Converse Relation
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if X and Y are sets and L \subseteq X \times Y is a relation from X to Y, then L^ is the relation defined so that yL^x if and only if xLy. In set-builder notation, :L^ = \. The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse. The unary operation that maps a relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally, induces a dagger category on the category of relations as detailed below. As a unary operation, taking the converse (sometimes called conversion or transposition) commutes with the order-relate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementary Domain
A complement is something that completes something else. Complement may refer specifically to: The arts * Complement (music), an interval that, when added to another, spans an octave ** Aggregate complementation, the separation of pitch-class collections into complementary sets * Complementary color, in the visual arts Biology and medicine *Complement system (immunology), a cascade of proteins in the blood that form part of innate immunity *Complementary DNA, DNA reverse transcribed from a mature mRNA template *Complementarity (molecular biology), a property whereby double stranded nucleic acids pair with each other *Complementation (genetics), a test to determine if independent recessive mutant phenotypes are caused by mutations in the same gene or in different genes Grammar and linguistics * Complement (linguistics), a word or phrase having a particular syntactic role ** Subject complement, a word or phrase adding to a clause's subject after a linking verb * Phonetic comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Closed Curve
In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere. While the theorem seems intuitively obvious, it takes some ingenuity to prove it by elementary means. ''"Although the JCT is one of the best known topological theorems, there are many, even among professional mathematicians, who have never read a proof of it."'' (). More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces. The Jordan curve theorem is named after the mathematician Camille Jordan (1838–1922), who found its first proof. For decades, mathematicians generally thought that this proof was flawed and that the first rigo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Curve Theorem
In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere. While the theorem seems intuitively obvious, it takes some ingenuity to prove it by elementary means. ''"Although the JCT is one of the best known topological theorems, there are many, even among professional mathematicians, who have never read a proof of it."'' (). More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces. The Jordan curve theorem is named after the mathematician Camille Jordan (1838–1922), who found its first proof. For decades, mathematicians generally thought that this proof was flawed and that the first rigo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homeomorphism
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word ''homeomorphism'' comes from the Greek words '' ὅμοιος'' (''homoios'') = similar or same and '' μορφή'' (''morphē'') = shape or form, introduced to mathematics by Henri Poincaré in 1895. Very roughly speaking, a topological space is a geometric object, and the homeomorphism is a continuous stretching and bending of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not. However, this desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Moritz Schönflies
Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology. Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland). Arthur Schoenflies married Emma Levin (1868–1939) in 1896. He studied under Ernst Kummer and Karl Weierstrass, and was influenced by Felix Klein. The Schoenflies problem is to prove that an (n - 1)-sphere in Euclidean ''n''-space bounds a topological ball, however embedded. This question is much more subtle than it initially appears. He studied at the University of Berlin from 1870 to 1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar to teach. Schoenflies was a frequent contributor to Klein's encyclopedia: In 1898 he wrote on set theory, in 1902 on kinematics, and on projective geometry in 1910. He was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Michigan
, mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As of October 25, 2021. , president = Santa Ono , provost = Laurie McCauley , established = , type = Public research university , academic_affiliations = , students = 48,090 (2021) , undergrad = 31,329 (2021) , postgrad = 16,578 (2021) , administrative_staff = 18,986 (2014) , faculty = 6,771 (2014) , city = Ann Arbor , state = Michigan , country = United States , coor = , campus = Midsize City, Total: , including arboretum , colors = Maize & Blue , nickname = Wolverines , sporti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States National Academy Of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the National Academy of Medicine (NAM). As a national academy, new members of the organization are elected annually by current members, based on their distinguished and continuing achievements in original research. Election to the National Academy is one of the highest honors in the scientific field. Members of the National Academy of Sciences serve '' pro bono'' as "advisers to the nation" on science, engineering, and medicine. The group holds a congressional charter under Title 36 of the United States Code. Founded in 1863 as a result of an Act of Congress that was approved by Abraham Lincoln, the NAS is charged with "providing independent, objective advice to the nation on matters related to science and technology. ... to provide scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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