Weak deformation retraction

Definition
Let $$X$$ be a topological space and $$A$$ a subspace of $$X$$. A weak deformation retraction from $$X$$ to $$A$$ is a homotopy $$F: X \times I \to X$$ such that:


 * $$F(x,0) = x \ \forall \ x \in X$$
 * $$F(a,t) \in A \ \forall \ a \in A, t \in I$$
 * $$F(x,1) \in A \ \forall \ x \in X$$