> [!definition] > > Let $X$ be a [[Topological Space|topological space]] and $A \subset X$, then a **deformation retraction** of $X$ onto $A$ is a [[Homotopy|homotopy]] relative to $A$ between $f_0 = \text{Id}_X$ and a [[Continuity|continuous]] map $f_1: X \to A$. > [!theorem] > > If there exists a deformation retraction of $X$ onto $A$, then the inclusion map $\iota: A \to X$ is a [[Homotopy Equivalence|homotopy equivalence]].