Strong deformation retract
This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces
Definition
A subspace of a topological space is termed a deformation retract if there is a homotopy between the identity map on the whole space, and a retraction onto the subspace, such that the map at every intermediate stage, restricts to identity on the subspace.