# Difference between revisions of "Manifold is not union of images of manifolds of smaller dimension"

Let $M$ be a smooth manifold and $N_1, N_2, \ldots$ be a countable sequence of smooth manifolds, each having dimension strictly less than that of $M$. Suppose $f_i:N_i \to M$ are smooth maps. Then, $M$ is not the union of $f_i(N_i)$.