Algebraic Topology · Problem 4.1.5

Homotopy Theory — Allen Hatcher

Mathematics — Topology · relative-homotopy-groups-cosets

Problem

For a pair

(X, A)

of path-connected spaces, show that

\pi_1(X, A, x_0)

can be identified in a natural way with the set of cosets

H\alpha

of the subgroup

H \subset \pi_1(X, x_0)

represented by loops in

A

x_0