Norm continuity of quasi-continuous mappings into C_p(X) and product spaces

摘要

A compact space X is said to have the NQ property if for every α-favorable space A and every quasi-continuous function φ : A → C_P(X), there is a dense G_δ subset D of A such that φ is norm continuous at each point of D. We give a game theoretic proof to show that the property NQ is closed under arbitrary product.