David Roberts
shrinkable map

A map $p:E\to B$ in $\mathrm{Top}$ is shrinkable if there is a section $s:B\to E$ such that $s\circ p$ is fibrewise homotopic to ${\mathrm{id}}_E$. That is, the homotopy $E\times I\to E$ covers the projection map ${\mathrm{pr}}_1:B\times I\to B$.