Whitehead's theorem states that a continuous map 
between nonempty connected CW-complexes is a homotopy
equivalence if, for a basepoint 
, it induces isomorphisms
of homotopy groups
 |
for every integer 
(Hatcher 2002, p. 346).
Whitehead's Theorem
See also
CW-Complex, Homotopy Group, IsomorphismExplore with Wolfram|Alpha
References
Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, p. 346, 2002. https://pi.math.cornell.edu/~hatcher/AT/AT.pdf.Referenced on Wolfram|Alpha
Whitehead's TheoremCite this as:
Weisstein, Eric W. "Whitehead's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WhiteheadsTheorem.html