Whitehead theorem
In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the concept of a CW complex that he introduced there. It is a model result of algebraic topology, in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping.
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Acyclic spaceAlgebraic topologyAspherical spaceCW complexClassifying space for U(n)Covering spaceFoliationGlossary of algebraic topologyHomotopy categoryJ. H. C. WhiteheadList of algebraic topology topicsList of theoremsNormal invariantPseudocircleRetraction (topology)Shape theory (mathematics)Weakly contractibleWhitehead's theoremWhitehead manifold
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Whitehead theorem
In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the concept of a CW complex that he introduced there. It is a model result of algebraic topology, in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping.
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En théorie de l'homotopie (une ...... lexes faite dans ces articles.
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In homotopy theory (a branch o ...... logical property of a mapping.
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У алгебричній топології теорем ...... ного ним поняття CW-комплексу.
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在數學領域代數拓撲學的同倫論中,懷特黑德定理說,拓撲空間X和 ...... 中證明,給出理由以他在論文所引入的CW複形概念作為研究對象。
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En théorie de l'homotopie (une ...... lexes faite dans ces articles.
@fr
In homotopy theory (a branch o ...... logical property of a mapping.
@en
У алгебричній топології теорем ...... ного ним поняття CW-комплексу.
@uk
在數學領域代數拓撲學的同倫論中,懷特黑德定理說,拓撲空間X和 ...... 中證明,給出理由以他在論文所引入的CW複形概念作為研究對象。
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Théorème de Whitehead
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Whitehead theorem
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Теорема Вайтхеда
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懷特黑德定理
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