Cao, JGauld, DBGreenwood, SMohamad, A2011-11-112011-11-1120082008New Zealand Journal of Mathematics, vol.37(1), pp.1 - 81171-6096https://hdl.handle.net/10292/2507Using topological games we investigate connections between properties of topological spaces and their spaces of continuous functions with the compact-open topology. This leads to new criteria for metrisability of a manifold. We show that a manifold M is metrisable if and only if a winning strategy applies to certain topological games played on C_k(M). We also show that M is metrisable if and only if C_k(M) is Baire, and even if and only if it is Volterra.New Zealand Journal of Mathematics is an open access journal. Authors retain the right to place his/her publication version of the work on a personal website or institutional repository for non commercial purposes. The definitive version was published in (see Citation). The original publication is available at (see Publisher’s Version).Banach-Mazur gameChoquet gameCompact-open topologyManifoldMetrisableMoving Off PropertyStrongly BaireBaireVolterraJournal ArticleOpenAccess