Question:
Nullhomotopic Mappings and Contractible Spaces
A space X is contractible if and only if every map f:X to Y (Y is arbitrary) is nullhomotopic. Similarly show X is contractible iff ever map f:Y to X is nullhomotopic.
In the first case if Y=X then see that the identity map on X is nullhomotopic. But Im not sure how to proceed for the rest.