Annals of Mathematical Sciences and Applications

We give an elementary proof of the Myers–Steenrod theorem, stating that the group of isometries of a connected Riemannian manifold $M$ is a Lie group acting smoothly on $M$. Our proof follows the approach of Chu and Kobayashi, but replacing their use of a theorem of Palais with a topological condition detecting when a locally compact subspace of $M$ is an embedded integral manifold of a given $k$-plane distribution.