In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between topological spaces X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence provided X and Y are connected and have the homotopy-type of CW complexes. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the CW complex concept that he introduced there.
Read more about Whitehead Theorem: Statement, Spaces With Isomorphic Homotopy Groups May Not Be Homotopy Equivalent, Generalization To Model Categories
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“Every philosophy is tinged with the colouring of some secret imaginative background, which never emerges explicitly into its train of reasoning.”
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