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:

• $F(x,0)=x\mathrm{\forall }x\in X$
• $F(a,t)\in A\mathrm{\forall }a\in A,t\in I$
• $F(x,1)\in A\mathrm{\forall }x\in X$