Sudden contracting homotopy

Definition
Let $$X$$ be a topological space. A sudden contracting homotopy on $$X$$ is a map $$F: X \times I \to X$$ such that:


 * $$F(x,0) = x \ \forall \ x \in X$$
 * For any $$t < 1$$, the map sending $$x$$ to $$F(x,t)$$ is a homeomorphism
 * There exists a point $$x_0 \in X$$ such that $$F(x,1) = x_0 \ \forall \ x \in X$$

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