函數(shù)一致連續(xù)性研究

函數(shù)1致連續(xù)性研究

摘要

本文通過幾個(gè)典型的例子對(duì)函數(shù)1致連續(xù)性的概念進(jìn)行深入分析，然后由康托定理出發(fā)討論函數(shù)1致連續(xù)性條件，得到幾個(gè)判別1致連續(xù)性的有用結(jié)論和方法，由判別函數(shù)1致連續(xù)性的方法得到證明函數(shù)在區(qū)間內(nèi)非1致連續(xù)的簡便方法，以加深了對(duì)函數(shù)1致連續(xù)性的概念的理解，最后總結(jié)1致連續(xù)函數(shù)的運(yùn)算性質(zhì)，包括復(fù)合函數(shù)的1致連續(xù)性及1致連續(xù)函數(shù)的4則運(yùn)算，使得對(duì)函數(shù)1致連續(xù)性的內(nèi)涵有了更全面，更深刻的理解和認(rèn)識(shí)。
關(guān)鍵詞：1致連續(xù)；函數(shù)；非1致連續(xù)；康托定理。

The research of Function uniform continuity

 

ABSTRACT

In this papers, We discuss uniform continuity of functions.The article carries on the thorough analysis through several typical example to the function uniform continuity concept. And then starting from Cantor theorem discussion function consistent continuity conditions. We get some useful conclusion and the method that distinguished the function whether identically continuously. Finally, we summarized the consistent continuous function operation nature. Including the uniform continuity of Composite function and the mathematical operations of consistent continuous function.
Keywords: Uniformly continuous; Function; Non- Uniformly continuous; Cantor theorem.

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