  Let $G$ be a matrix group. Topological $G$-manifolds with Palais-proper
action have the $G$-homotopy type of countable $G$-CW complexes (3.2). This
generalizes E Elfving's dissertation theorem for locally linear $G$-manifolds
(1996). Also we improve the Bredon--Floyd theorem from compact groups $G$
(1960).
