# Nullhomotopic Mappings and Contractible Spaces

I am having problems proving this fact. 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.

https://brainmass.com/math/synthetic-geometry/nullhomotopic-mappings-contractible-spaces-112848

#### Solution Preview

Notation: We let c_x:X ->{x} denote the constant map to {x}.

"o" is composition, "~" is "homotopic to", $1_X$ identity on X

Suppose that X is ...

#### Solution Summary

Nullhomotopic Mappings and Contractible Spaces are investigated.

$2.19