Definition 5

Let X be a topological space and let A be a subset of X. A contraction of X onto A is a homotopy $\sigma : X\times \mathbf{I}\rightarrow X$ fixed on A whose origin is the identity mapping of X and whose term is a retraction of X onto A. If there exists a contraction of X onto A, one says that X can be contracted onto A, or again that A is a retractile subset of X.