Selections, games and metrisability of manifolds

Abstract

In this note we relate some selection principles to metrisability and separability of a manifold. In particular we show that ${\mathsf{S}}_{\mathsf{fin}}(\mathcal{K},\mathcal{O})$, ${\mathsf{S}}_{\mathsf{fin}}(\mathsf{\Omega },\mathsf{\Omega })$ and ${\mathsf{S}}_{\mathsf{fin}}(\mathsf{\Lambda },\mathsf{\Lambda })$ are each equivalent to metrisability for a manifold, while ${\mathsf{S}}_1(\mathcal{D},\mathcal{D})$ is equivalent to separability for a manifold.

9 pages

References in corpus (1)

• Metrisability of Manifolds