Definition:Homotopy/Null-Homotopic

Definition
Let $X$ and $Y$ be topological spaces. Let $f: X \to Y$ be a continuous mapping.

Then:
 * $f$ is nulhomotopic


 * there exists a constant mapping $g: X \to Y$ such that $f$ and $g$ are freely homotopic.
 * there exists a constant mapping $g: X \to Y$ such that $f$ and $g$ are freely homotopic.

Also known as
Some texts spell this as nullhomotopic.

Some texts hyphenate the above: null-homotopic.