Hilbert cube manifolds of maps

The purpose of this note is to illustrate in the simplest possible terms how a function space may be a Hilbert Cube (= Q) manifold. It is shown that certain spaces of “rectifiable” maps from a compact Riemannian manifold to a flat Kiemannian manifold are Q-manifolds. For example: if α > 0, the space of loops of length ⩽α in a flat manifold is a Q-manifold. No prior knowledge of Riemannian geometry is required.