拓扑代数系统中的一类连续与极限

Continuity and Limit in the Topological Algebra System

引入了映射基于某个拓扑空间的连续和极限的定义,精确的推广了数学分析中度量空间里连续和极限的概念.文中证明了这种基于某个拓扑空间的连续性是具有代数运算封闭性的,而且映射极限是可保持代数运算的一些主要性质,将度量空间上的函数连续和极限的相关性质推广到了以拓扑代数系统为值域的情况.

This paper introduces the definitions of continuity and limit of a mapping based on a topological space,and generalizes the concepts of continuity and limit precisely in the metric space. It proves that the continuity based on a topological space has algebraic closed nature and the mapping limit is important property for the algebraic operation, which extends the property of continuity and limit of the metric space to the topological algebra system.