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 ( f n ) n ∈ ω of functions f n : 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.

中文翻译：

---

一些收敛函数序列的一致收敛点集的刻画

我们表征了在完全法线空间上定义的实值函数的逐点收敛序列的一致收敛点集。我们证明，如果X是一个完全正态空间，并且可以由密集子集和A⊆X的不相交序列覆盖，则A是函数fn的某些收敛序列（fn）n∈ω的一致收敛点集。 ：X→ℝ当且仅当A是包含所有X的孤立点的Gδ-集合。该结果推广了2019年发表的JánBorsík定理。