Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. Algebraic topology can be used in a number of other fields such as physics, branches of geometry and...
simple.wikipedia.org/wiki/Algebraic_topologyAlgebraic Topology Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that remain invariant under...
mathworld.wolfram.com/AlgebraicTopology.htmlAlgebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces.en.wikipedia.org/wiki/Category:Algebraic_topology- 其他用户还问了以下问题
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前往 Wikipedia 查看全部内容Algebraic topology - Wikipedia
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily … 展开
Below are some of the main areas studied in algebraic topology:
Homotopy groups
In mathematics, homotopy groups are used in algebraic topology … 展开An older name for the subject was combinatorial topology, implying an emphasis on how a space X was constructed from simpler … 展开
Classic applications of algebraic topology include:
• The Brouwer fixed point theorem: every continuous map … 展开In general, all constructions of algebraic topology are functorial; the notions of category, functor and natural transformation originated here. Fundamental groups and homology and cohomology groups are not only invariants of the underlying … 展开
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Topology - Wikipedia
网页Algebraic topology is a branch of mathematics that uses tools from algebra to study topological spaces. [13] The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, …
Chain (algebraic topology) - Wikipedia
网页In algebraic topology, a k - chain is a formal linear combination of the k -cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k -chains are …
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Category:Algebraic topology - Wikipedia
网页Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces
Algebraic topology (object) - Wikipedia
网页Algebraic topology (object) In mathematics, the algebraic topology on the set of group representations from G to a topological group H is the topology of pointwise …
Glossary of algebraic topology - Wikipedia
网页This is a glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory, …
Algebraic Topology - MIT Mathematics
网页In algebraic topology, we investigate spaces by mapping them to algebraic objects such as groups, and thereby bring into play new methods and intuitions from algebra to answer …
Algebraic topology - Simple English Wikipedia, the free encyclopedia
网页Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. Algebraic topology can be used in a number of other fields …
Algebraic topology - Encyclopedia of Mathematics
网页2023年10月28日 · Algebraic topology. The branch of mathematics in which one studies such properties of geometrical figures (in a wider sense, of all objects for which one can …
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