| 关于函数连续性的再研究 |
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| 引用本文： | 董立华.关于函数连续性的再研究[J].菏泽学院学报,2013(5):5-7. |
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| 作者姓名： | 董立华 |
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| 作者单位： | 德州学院数学科学学院,山东德州253023 |
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| 基金项目： | 基金项目：山东省“十二·五”教育科学规划项目（2011JG441）;德州学院教学改革研究重点项目（JGLX-A1108） |
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| 摘 要： | 指出函数连续与可导具有严格的一点对一点特征，并通过实例说明确实存在着处处连续而处处不可导的函数．其中函数的连续性、近似连续性、对称连续性均是对函数某点性质的刻画，且容易证明函数连续一定对称连续，也是近似连续的，反之不然．
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| 关 键 词： | 函数连续 对称连续 近似连续 |
A Restudy on the Continuity of Functions |
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| Institution: | Dong Li - hua (College of Mathematical Sciences, Dezhou University, Dezhou Shandong 253023, China) |
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| Abstract: | The continuity and differentiability of functions possess the strict point to point character. By actual examples, we explain that there exist functions which are continuous but non differentiable everywhere. The conti- nuity, approximate continuity and symmetric continuity describe the property of a point of functions. We also prove that, the continuity imply symmetric and approximate continuity, but not vice versa. |
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| Keywords: | functions continuous symmetric continuous approximate continuous |
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