GAMES AND METRISABILITY OF MANIFOLDS

Jiling Cao, David Gauld, Sina Greenwood, Abdul Mohamad
2008 NEW ZEALAND JOURNAL OF MATHEMATICS   unpublished
Using 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 mani-fold. 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.
fatcat:p2cw4fvfhrbthlj5ciaafe7ipy