Hey, before I write this up I just am curious if anyone knows if the following is correct.

Theorem:Let $\displaystyle \left\{\mathfrak{M}_n\right\}_{n\in\mathbb{N}}$ be a class of $\displaystyle m$-manifolds. Then, $\displaystyle \mathfrak{M}=\coprod_{n=1}^{\infty}\mathfrak{M}_n$ is an $\displaystyle m$-manifold under the coproduct topology.

Right?