A characterization of the uniform convergence points set of some convergent sequence of functions

Abstract

We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X, then A is the set of points of the uniform convergence for some convergent sequence (fn)n∈ω of functions fn : X → R if and only if A is G δ -set which contains all isolated points of X. This result generalizes a theorem of Ján Borsík published in 2019.