Oscillations, Quasi-oscillations and Joint Continuity

Parallel to the concept of quasi-separate continuity, we define a notion for quasi-oscillation of a mapping f : X × Y → R. We also introduce a topological game on X to approximate the oscillation of f . It follows that under suitable conditions, every quasi-separately continuous mapping f : X×Y → R has the Namioka property. An illuminating example is also given.