Remark 3

Let A and B be topological spaces, let $a$ be a point of A, and let $f: A\rightarrow B$ be a continuous mapping. Put $b=f(a)$. If H is an admissible subgroup of $\pi_1(B, b)$, its inverse image under the homomorphism $\pi_1(f, a)$ is an admissible subgroup of $\pi_1(A, a)$. Consequently, the group homomorphism $\pi_1(f, a):\pi_1(A, a)\rightarrow \pi_1(B, b)$ is continuous, when these groups are endowed with the admissible topology.