Algebraic Topology · Problem 4.1.3

Homotopy Theory — Allen Hatcher

Mathematics — Topology · h-spaces-homotopy-groups

Problem

For an H-space

(X, x_0)

with multiplication

\mu: X \times X \to X

, show that the group operation in

\pi_n(X, x_0)

can also be defined by the rule

(f + g)(x) = \mu(f(x), g(x))