有界连续无处局部uniformly continuous函数集不是Borel
The set of bounded continuous nowhere locally uniformly continuous functions is not Borel
摘要：
对于无处局部紧度量空间$X$，$X$上的有界连续、无处局部一致连续实值函数集在上确界范数下包含$X$上的所有有界连续实值函数空间$C_b(X)$中的稠密$G_δ$集.此外，当$X$是可分的时，$X$上的有界连续、无处局部一致连续的实值函数集本身就是一个$G_δ$集。我们表明，相比之下，当$X$是不可分的，这组功能甚至不是一个博雷尔集。
英文摘要：
It is known that for $X$ a nowhere locally compact metric space, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $X$ contains a dense $G_δ$ set in the space $C_b(X)$ of all bounded continuous real-valued functions on $X$ in the supremum norm. Furthermore, when $X$ is separable, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $X$ is itself a $G_δ$ set. We show that in contrast, when $X$ is nonseparable, this set of functions is not even a Borel set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
