基于偏序集的连续映射  

Continuous Mapping Based on Poset

作　　者：杨大子 邹志伟 YANG Dazi;ZOU Zhiwei(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2024年第1期60-65,89,共7页Journal of University of South China：Science and Technology

基　　金：湖南省教育厅科研基金项目(22B0447)。

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。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.

关 键 词：偏序集 邻域 极限 连续性 

分 类 号：O153.1[理学—数学]