Contracting homotopy

Definition
Let $$X$$ be a topological space. A contracting homotopy for $$X$$ is a homotopy $$F: X \times I \to X$$ such that there exists a point $$x_0 \in X$$ such that:


 * $$F(x,0) = x \ \forall \ x \in X$$
 * $$F(x,1) = x_0 \ \forall \ x \in X$$

A topological space which has a contracting homotopy is termed a contractible space.