连续函数的概念和性质剖析及其拓展教学研究

On the Concept,Nature and Expansion of Continuous Functions

比较深入的剖析了连续函数的概念,对连续函数的三种常见定义方式进行了分析,以连续性的判断为例,分析了数学思维的特点,介绍了一个一般文献中不常见的重要结论,讨论了连续函数概念在理论、应用和数学概念进一步发展的拓展.

This paper discusses the concept of continuous functions, and their three common definitions. Using the three criteria for continuity, we analyze the characteristics of mathematical thinking, introduce an important conclusion which is not commonly appeared in the literature, and discuss the expansion of the concept of continuous functions used in the theory, application, and further mathematical development.