Fig. 8.

The homotopy $H_{\tau }$ takes y linearly into z and $H_{{\tau }^{\prime }}$ takes y into $z^{\prime }$. Due to the symmetry represented by the horizontal line, $|p{f}^{\prime }|$ maps $H_{\tau }(y,t)$ into the same point of X as $|p{f}^{\prime }|H_{{\tau }^{\prime }}(y,t)$