Semi-sudden homotopy

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


 * For any $$x$$, $$F(x,0) = x$$
 * For any $$t < 1$$ the map $$x \mapsto F(x,t)$$ is a homeomorphism from $$X$$ to whatever its image is under the map

Stronger properties

 * Sudden homotopy