The Whitehead Theorem states that a continuous map between CW complexes that induces an isomorphism on every homotopy group is in fact a homotopy equivalence. Named for J. H. C. Whitehead, it is a foundational result of algebraic topology that justifies studying spaces through their homotopy groups.
Facts
StatementA continuous map between CW complexes that induces an isomorphism on every homotopy group is a homotopy equivalence. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Whitehead Theorem (Wikipedia)
Wikimedia FoundationLead paragraph, statement sentence
In homotopy theory, 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.
Lead paragraph, history sentence
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.
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