algebraic topology

Math.the branch of mathematics that deals with the application of algebraic methods to topology, esp. the study of homology and homotopy.
* * *
Field of mathematics that uses algebraic structures to study transformations of geometric objects.It uses functions (often called maps in this context) to represent continuous transformations (see topology). Taken together, a set of maps and objects may form an algebraic group, which can be analyzed by grouptheory methods. A wellknown topic in algebraic topology is the fourcolour map problem.* * *
Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses functions (often called maps in this context) to represent continuous transformations (see topology). Taken together, a set of maps and objects may form an algebraic group, which can be analyzed by grouptheory methods. A wellknown topic in algebraic topology is the fourcolour map problem.* * *
Universalium. 2010.
Look at other dictionaries:
Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… … Wikipedia
algebraic topology — Math. the branch of mathematics that deals with the application of algebraic methods to topology, esp. the study of homology and homotopy … Useful english dictionary
algebraic topology — noun That branch of topology that associates objects from abstract algebra to topological spaces … Wiktionary
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 convergence, i.e. pi converges to p if the limit of pi ( g ) = p ( g ) for every g in G .This terminology is… … Wikipedia
Directed algebraic topology — In mathematics, directed algebraic topology is a form of algebraic topology that studies topological spaces equipped with a family of directed paths, closed under some operations. The term d space is applied to these spaces. Directed algebraic… … Wikipedia
List of algebraic topology topics — This is a list of algebraic topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of geometric topology topics Publications in topology Topological property Contents 1… … Wikipedia
Chain (algebraic topology) — This article is about algebraic topology. For the term chain in order theory, see chain (order theory). In algebraic topology, a simplicial k chain is a formal linear combination of k simplices.[1] Integration on chains Integration is defined on… … Wikipedia
Moore space (algebraic topology) — See also Moore space for other meanings in mathematics. In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of… … Wikipedia
Induced homomorphism (algebraic topology) — In mathematics, especially in the area of topology known as algebraic topology, an induced homomorphism is a way of relating the algebraic invariants of topological spaces which are already related by a continuous function. Such homomorphism… … Wikipedia
Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… … Wikipedia