| 基于偏序集的连续映射 |
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| 引用本文： | 杨大子,邹志伟.基于偏序集的连续映射[J].南华大学学报(自然科学版),2024(1):60-65, 89. |
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| 作者姓名： | 杨大子 邹志伟 |
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| 作者单位： | 南华大学 数理学院,湖南,衡阳,421001 |
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| 基金项目： | 湖南省教育厅科研基金项目(22B0447) |
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| 摘 要： | 基于实数集R的经典邻域的概念,引入了一个新的基于偏序集P的邻域的概念,随后定义了一个从P到R的映射的极限和连续的新概念,并在偏序集的背景下验证了连续函数的各种经典结论,例如有界性、介值定理等等。
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| 关 键 词： | 偏序集 邻域 极限 连续性 |
| 收稿时间： | 2023/10/18 0:00:00 |
Continuous Mapping Based on Poset |
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| YANG Dazi,ZOU Zhiwei.Continuous Mapping Based on Poset[J].Journal of Nanhua University:Science and Technology,2024(1):60-65, 89. |
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| Authors: | YANG Dazi ZOU Zhiwei |
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| Institution: | School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China |
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| Abstract: | Different from the classical neighborhood based on real number set R, this paper introduces we introduce a new notion of neighborhood based on a poset P. Subsequently, the novel notions of limit and continuity of a mapping from P to R are also defined. Various classical results about a continuous functions are verified in the context of poset in this paper, such as boundness, intermediate value theorem and etc. |
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| Keywords: | poset neighborhood limit continuity |
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