闭区间上连续函数的性质及其推广

The properties and generalization of continuous function on closed intervalAbstract In our study and life,we often encounter the most basic function-continuousfunction.In the mathematics of junior and senior high school,almost all of the functions weencounter are continuous functions,but these basic functions have many excellent properties,especially the continuous function on the closed interval,which has many properties that theopen interval does not have.Therefore,it is necessary to understand the continuous functionon the closed interval.In order to solve the properties of the continuous function on the closedinterval,we must start from what is the continuous function,and to know what is thecontinuous function,we must first understand the function limit.So this paper starts from thefunction limit,introduces the definition of the function limit,the properties of the function limit,the definition of the continuity of the function,and the properties of the continuous functionQuality,then introduce the properties of continuous function on closed interval,and finallyenumerate the generalization of continuous function properties on closed interval,such as thegeneralization of the most value theorem,the generalization of intermediate value theorem,the generalization of bounded theorem,the generalization of zero point theorem,thegeneralization of the existence theorem of root,etc.,and analyze and compare thegeneralization of these theorems.This paper will compare them from two aspects The secondis the conclusion comparison.Finally,some conclusions about the extension of continuousfunction properties on closed interval are summarized.Key words:The extension of the properties of continuous function on closed intervalproperties of continuous functions on closed intervals continuous function