Selections, games and metrisability of manifolds

In this note we relate some selection principles to metrisability and separability of a manifold. In particular we show that $\sf{S}{fin}(\mathcal K,\mathcal O)$,$\sf{S}{fin}(\Omega,\Omega)$and$\sf{S}_{fin}(\Lambda,\Lambda)$ are each equivalent to metrisability for a manifold, while ${\mathsf{S}}_{\mathsf{1}}(\mathcal{D},\mathcal{D})$ is equivalent to separability for a manifold.