Space in which every retraction is a deformation retraction

Definition
A space in which every retraction is a deformation retraction is a topological space $$X$$ with the property that any retraction math>r:X \to Y for a subspace $$Y$$ of $$X$$ (with the subspace topology) arises as a deformation retraction, i.e., there is a homotopy from the identity map to that retraction that restricts to $$r$$ on the subspace $$Y$$ at all time.