algebraic topology oor Sjinees
algebraic topology
en
That branch of topology that associates objects from abstract algebra to topological spaces.
Vertalings in die woordeboek Engels - Sjinees
代数拓扑
en
branch of mathematics
into a subject which is now called algebraic topology.
如今被称作 代数拓扑的学科
Geskatte vertalings
Vertoon algoritmies gegenereerde vertalings
voorbeelde
Advanced filtering
Voorbeelde moet herlaai word.
For example, Henri Poincaré founded what is now called algebraic topology by introducing the fundamental group.
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In general, all constructions of algebraic topology are functorial; the notions of category, functor and natural transformation originated here.
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Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick."
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Norman Earl Steenrod (April 22, 1910 – October 14, 1971) was a mathematician most widely known for his contributions to the field of algebraic topology.
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Classic applications of algebraic topology include: The Brouwer fixed point theorem: every continuous map from the unit n-disk to itself has a fixed point.
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He co-invented Spanier–Whitehead duality and Alexander–Spanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology (Spanier 1981).
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Together with Hirzebruch, he laid the foundations for topological K-theory, an important tool in algebraic topology, which, informally speaking, describes ways in which spaces can be twisted.
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In mathematics, the Serre spectral sequence (sometimes Leray-Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology.
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Peter May, "A Concise Course in Algebraic Topology" : chapter 6 defines and discusses cofibrations, and they are used throughout Ronald Brown, "Topology and Groupoids" ; Chapter 7 is entitled "Cofibrations", and has many results not found elsewhere.
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This thesis firmly established in algebraic topology the use of spectral sequences, and clearly separated the notions of fiber bundles and fibrations from the notion of sheaf (both concepts together having been implicit in the pioneer treatment of Jean Leray).
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Texts on modal logic typically do little more than mention its connections with the study of Boolean algebras and topology.
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This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by PG(2, R), RP2, or P2(R), among other notations.
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Milnor was awarded the 2011 Abel Prize, for his "pioneering discoveries in topology, geometry and algebra."
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These issues are studied in pointless topology, where complete Heyting algebras are also called frames or locales.
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This result is quite interesting, because the statement is purely algebraic yet the simplest known proof is topological.
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James writes in : Algebraic topology underwent a spectacular development in the years following the second world war.
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This latter work is an introduction to algebraic topology for a reader without background in general topology .
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Algebraic topology: a student's guide (1972) is rather unusual.
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After his first research work on point-set topology Steenrod then worked on algebraic topology.
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However, he was most strongly influenced by Henry Whitehead , who led the foremost British school of algebraic topology.
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In doing this he developed a theory of algebraic topology of algebraic varieties of higher dimension.
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... for his fundamental work in algebraic topology, differential geometry and differential topology.
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He decided to work on algebraic topology and his work was supervised by M M Postnikov.
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In the 1950s Milnor did a substantial amount of work on algebraic topology which is discussed in .
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James published Handbook of algebraic topology in 1995.
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