论文标题
某些收敛序列的均匀收敛点集的表征
A characterization of the uniform convergence points set of some convergent sequence of functions
论文作者
论文摘要
我们表征了在完美正常空间上定义的实值函数的圆角收敛序列的均匀收敛点集。我们证明，如果$ x $是一个完全正常的空间，可以通过一系列密集子集和$ a \ subseteq x $覆盖，那么$ a $是某些收敛序列$（f_n）_ {n \ in的ω} $ function $ f_n：x $ f_ a $ $ g y $ n $ if的均匀序列$（f_n）_ {n \ income）所有$ x $的隔离点。该结果概括了JánBorsík定理于2019年出版。
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 $A\subseteq X$, then $A$ is the set of points of the uniform convergence for some convergent sequence $(f_n)_{n\inω}$ of functions $f_n:X\to \mathbb R$ 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.
