Definition:Homotopy/Path

Definition
Let $X$ be a topological space.

Let $f, g: \closedint 0 1 \to X$ be paths.

Then:
 * $f$ and $g$ are path-homotopic


 * $f$ and $g$ are homotopic relative to $\set {0, 1}$.
 * $f$ and $g$ are homotopic relative to $\set {0, 1}$.

Also see

 * Path-Homotopic Paths have Path Homotopy
 * Homotopic Paths have Same Endpoints
 * Relative Homotopy is Equivalence Relation