# Covering spaces, R^n, homomorphism

Let $A$ be a subset of $R^n$ . let $h : (A, a_0) \rightarrow (Y, y_0)$ . show that if $h$ is extendable to a continuous map of $R^n$ into $Y$, then $h_*$ is the zero homomorphism. (the trivial homomorphism that maps everything to the identity element)
Hint: Let $[f]\in \pi_1(A,a_0)$. Show that $h\circ f$ is nullhomotopic.