Theorem

Whitehead Theorem

Topology

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

Statement

A continuous map between CW complexes that induces an isomorphism on every homotopy group is a homotopy equivalence. 1

Proof Year

1949 1

Classification

Statement Form

Characterization Theorem 1

Connections

Source Whitehead Theorem (Wikipedia)

Sources

1. Whitehead Theorem (Wikipedia)

Wikimedia Foundation

Lead section
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.
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.
Proved By: J. H. C. Whitehead, Lead
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.
In Group: Algebraic Topology, Lead paragraph
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.

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Whitehead Theorem

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