contractible (i.e. the identity map is null-homotopic).
*X is homotopy equivalent to a one-point space.
*X deformation retracts onto a point. (However, there exist contractible spaces which do not strongly deformation retract to a point.)
*For any path-connected space Y, any two maps f,g: X -> Y are homotopic.
*For any nonempty space Y, any map f: Y -> X is null-homotopic.

The cone on a space X is always contractible. Therefore