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| algebraic topology ： ウィキペディア英語版 |
algebraic topology
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 uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.
==Main branches of algebraic topology==
Below are some of the main areas studied in algebraic topology:
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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