Covering spaces, R^n, homomorphism

• May 17th 2011, 11:40 PM
aharonidan
Covering spaces, R^n, homomorphism
Hello all,
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)

thanks
• May 21st 2011, 07:24 PM
ojones
Hint: Let $[f]\in \pi_1(A,a_0)$. Show that $h\circ f$ is nullhomotopic.