On page 330 of John G. Ratcliffe's text on hyperbolic manifolds, he defines a manifold $M$ to be a locally Euclidean Hausdorff space. By locally Euclidean, he means as usual that for each $x \in M$ there is an open neighbour $U$ of $x$ which is homeomorphic to an open subset of $\mathbb{R}^n$.
But he omits the usual paracompactness assumption. I would guess that $M$ being locally Euclidean and Hausdorff is not sufficient to imply that it is paracompact, given this problem from Lee's book.
Does anyone know of such a counterexample?