| 实数连续性的16个等价命题 |
| |
| 引用本文： | 王敏生.实数连续性的16个等价命题[J].安徽师范大学学报(自然科学版),2012,35(3):205-210. |
| |
| 作者姓名： | 王敏生 |
| |
| 作者单位： | 安徽师范大学数学计算机科学学院,安徽芜湖,241000 |
| |
| 摘 要： | 以十进位小数表示为出发点,借助连续归纳法把实数连续性常用的7个等价命题扩充到16个等价命题,其中包括有界闭集上连续函数的三大性质,这充分显示了实数连续性在整个数学分析中的重要地位和作用.
|
| 关 键 词： | 连续性 连通性 完全覆盖 连续归纳法 |
Sixteen Equivalent Propositions of Real Number Continuity |
| |
| Wang Min-sheng.Sixteen Equivalent Propositions of Real Number Continuity[J].Journal of Anhui Normal University(Natural Science Edition),2012,35(3):205-210. |
| |
| Authors: | Wang Min-sheng |
| |
| Institution: | Wang Min-sheng(College of Mathematics and Computer Science,Anhui Normal University, Wuhu 241003,China) |
| |
| Abstract: | This paper,starting from decimal number expressions,by using real number continuous induction,increases the common 7 equivalent propositions to 16 equivalent propositions,including three features of the continuous function in a bounded closed set,which illustrates the important position and role of real number continuity in the overall mathematics analysis. |
| |
| Keywords: | continuity connectivity full-covering continuous induction |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
