论文标题
同时扩展连续和均匀连续函数
Simultaneous Extension of Continuous and Uniformly Continuous Functions
论文作者
论文摘要
勒贝格（Lebesgue）于1907年获得了第一个已知的连续扩展结果。1915年，Tietze发表了他著名的扩展定理定理Lebesgue从飞机到一般度量空间的结果。他通过涉及度量空间距离函数的明确公式构建了扩展。此后，几位作者贡献了其他明确的伸展公式。在本文中，我们表明所有这些扩展结构也保留了统一的连续性，这回答了圣沃森提出的一个问题。实际上，对于特殊有限的功能，这种结构是同时发生的。基于此，我们还通过构建了保留均匀连续性的各种连续（非线性）扩展运算符来完善Dugundji的结果。
The first known continuous extension result was obtained by Lebesgue in 1907. In 1915, Tietze published his famous extension theorem generalising Lebesgue's result from the plane to general metric spaces. He constructed the extension by an explicit formula involving the distance function on the metric space. Thereafter, several authors contributed other explicit extension formulas. In the present paper, we show that all these extension constructions also preserve uniform continuity, which answers a question posed by St. Watson. In fact, such constructions are simultaneous for special bounded functions. Based on this, we also refine a result of Dugundji by constructing various continuous (nonlinear) extension operators which preserve uniform continuity as well.
