Points of uniform convergence and quasicontinuity

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 Gδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\delta }$$\end{document}-set containing all isolated points. On the other hand, an arbitrary Gδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{\delta }$$\end{document}-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.