| 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.[YANG Dazi,ZOU Zhiwei.Continuous Mapping Based on Poset[J].Journal of University of South China(Science and Technology),2024,(1):60~65, 89.] |
| 基于偏序集的连续映射 |
| Continuous Mapping Based on Poset |
| 投稿时间：2023-10-18 |
| DOI： |
| 中文关键词: 偏序集 邻域 极限 连续性 |
| 英文关键词:poset neighborhood limit continuity |
| 基金项目:湖南省教育厅科研基金项目(22B0447) |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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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