Locally uniformly continuous functions
Locally uniformly continuous functions
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局部一致连续函数
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Alexander J. Izzo
中科院分区：
文献类型：
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作者：
Alexander J. Izzo
证明了在无限维可分赋范空间上存在处处局部一致连续的连续实值函数。给出了1P（1 < p < cc）上的一个显式例子。本文还证明了度量空间上的每个连续实值函数都可以用局部一致连续函数一致逼近。
It is shown that on every infinite-dimensional separable normed space there exist continuous real-valued functions that are nowhere locally uniformly continuous. An explicit example of such a function on 1P (1 < p < cc) is given. It is also shown that every continuous real-valued function on a metric space can be approximated uniformly by locally uniformly continuous functions.