度量空间上泛函的一致连续性

Uniform Continuity of Functional on Metric Space

定义了度量空间上泛函的一致连续性以及一致连续性的判定函数,研究了判定函数的性质,建立了判定函数和泛出一致连续的关系,利用判定函数给出了度量空间和次范整线性空间上泛函一致连续的一个充分必要条件,使得泛函一致连续性的判定变得简单。

In this paper, we introduce the uniform continuity of functional on a metric space and the test function of a uniform continuity. The character of test function and the relation between the test function and the uniform continuity is studied. Using the test function, we obtain a necessary and sufficient condition of determining the uniform continuity of functional on a metric space or a sub - normed Z - linear space. In this case, it is simple to determine the uniform continuity of functional