基于偏序集的连续映射

Continuous Mapping Based on Poset

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.