Deformation and deformation retraction

Let \(X\) be a topological space and \(I=[0,1]\). A deformation of \(X\) is a family of maps \(f_t\colon X\to X\), \(t\in I\), such that \(f_0=\id_X\) and \((x,t)\mapsto f_t(x)\) is a continuous map \(X\times I\to X\). For a subspace \(A\subseteq X\), a deformation retraction of \(X\) onto \(A\) is a deformation \((f_t)_{t\in I}\) of \(X\) with \(f_1(X)=A\) and \(f_t(a)=a\) for all \(a\in A\) and \(t\in I\) [@Hat02].