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Dictionary

Words, grammatical forms and meanings linked to the ontology.

algebraic topology en · NOUN

Meanings

  1. (uncountable) The branch of mathematics that uses tools from abstract algebra to study topological spaces.
    • The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology. 2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii:
    • 1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company, Professor Emil Artin lectured on algebraic topology during the winter semester of 1959–60.
    • Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.
    • The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).

Relateds

differential topology · algebraic geometry

Synonyms

combinatorial topology (branch of mathematics)

Translations (7)

de algebraische Topologie (branch of mathematics) · pl topologia algebraiczna (branch of mathematics) · it topologia algebrica (branch of mathematics) · el αλγεβρική τοπολογία (branch of mathematics) · fi algebrallinen topologia (branch of mathematics) · hy հանրահաշվական տոպոլոգիա (branch of mathematics) · pt topologia algébrica (branch of mathematics)