Points of uniform convergence and quasicontinuity

Abstract

Sets of points of uniform convergence for sequences of quasicontinuous functions and for convergent sequences of functions are characterized. It is proved that a subset of a metric space is the set of points of uniform convergence for some convergent sequence of functions if and only if it is a $$G_{\delta }$$ -set containing all isolated points. On the other hand, an arbitrary $$G_{\delta }$$ -set is equal to the set of points of uniform convergence of some sequence of quasicontinuous functions. In conclusion, a new characterization of Baire spaces in the class of all metric spaces is given.