函数在区间上连续的充要条件

The Sufficient and Necessary Conditios for a Function to Continue on Intervals

本文从函数的介值性出发,给出并证明了函数在区间上连续的三个充要条件,并运用这些条件,对数学分析中的一些函数连续性的命题,给出了新的较为简明的证明。

This paper gives and proves the three sufficient and necessary conditions for a function to continue on intervals in the light of a function being an intermediate value. And the paper makes use of such conditions to give out some new and simpler proofs to the proposi-on concerning the functional continuation in mathematical analyses.