85教育研究2013年第36期关于一致连续的概念与性质的若干探究郭占海(河套学院理学系 内蒙古 巴彦淖尔 015000)【摘要】 函数一致连续是连续的特殊情况, 也是学习 的难点。 另 外函数在一点连续, 那么和、 差、 积、 商也连续。 函数一致连续它的和差积商是否是一致连续? 本文对函数连续概念与已知连续概念进行探讨, 也研究了 一致连续函数的和差积商的一些性质。【关键词】 一致连续 ; 定义 ; 性质【中图分类号】 G642 【文献标识码】 B 【文章编号】 2095-3089(2013) 36-0085-01 2 δ<\ue070\ue003 \ue0a7\ue09c\ue0ba\ue056\ue097\ue031\ue061\ue0aa\ue096\ue0bc\ue074\ue078\ue098\ue030\ue089\ue0bd\ue021\ue060\ue024\ue003 \ue018\ue098\ue0b2\ue010\ue0a1\ue0b1\ue087\ue003 \ue02b\ue065\ue0a7\ue051\ue03c\ue0a7\ue09e\ue086\ue003 \ue083\ue071\ue05b\ue09a\ue098\ue08a\ue09c\ue0ba\ue056\ue097\ue005 \ue09c\ue0ba\ue056\ue097\ue0aa\ue056\ue097\ue021\ue055\ue08b\ue0aa\ue067\ue00e\ue074\ue071\ue05b\ue005 \ue022\ue022\ue003 \ue07a\ue0a0\ue0a7\ue00c\ue09a\ue029\ue09c\ue0ba\ue056\ue097\ue049\ue095\ue099\ue04c\ue000\ue002\ue001 \ue002\ue00e\ue010\ue00c\ue003\ue010\ue00c\ue00b\ue007\ue004\ue000\ue026\ue0a2 1 0,0εδ∀ >∃>\ue001 \ue081\ue0a5 \ue021\ue006 \ue002 \ue00312,,x xI∀∈12,xxδ−<\ue0a712( )f x()f xε−<\ue0b0\ue015( )f x \ue0af\ue067\ue041 I\ue09c\ue0ba\ue056\ue097\ue000\ue026\ue0a2 2 0,0εδ∃∀ >>\ue003:,x xaδ∀−<\ue0a7( )f x( )f aε−<\ue0b0\ue015( )f x \ue0af\ue024 a \ue01a\ue056\ue097\ue003 \ue06bf x \ue0af I\ue056\ue097\ue000\ue0c0:\ue001 1\ue002 \ue0a6\ue026\ue0a2\ue050\ue0b6\ue003 \ue09c\ue0ba\ue056\ue097\ue00c\ue056\ue097\ue003 \ue02d\ue0b7\ue003 \ue056\ue097\ue010\ue09c\ue026\ue09c\ue0ba\ue056\ue097\ue000 \ue07a\ue0a0\ue09c\ue0ba\ue056\ue097\ue074\ue056\ue097\ue0af\ue080\ue042\ue043\ue064\ue08c\ue021\ue07d\ue076\ue000\ue001 2\ue002 \ue056\ue097\ue074\ue04d\ue012\ue031\ue061\ue003 \ue02b\ue09c\ue0ba\ue056\ue097\ue074\ue0b3\ue07f\ue031\ue061\ue003 \ue06b\ue039\ue078\ue067\ue041 I\ue021\ue05c\ue09c\ue024\ue028\ue0a7\ue091\ue0a4\ue021\ue0b4\ue078\ue006\ue001 \ue040\ue06f\ue007 \ue035\ue026\ue002 \ue003( )f x \ue0af\ue067\ue041 I \ue06d\ue05c\ue09c\ue024\ue028\ue056\ue097\ue000 \ue015( )( )f x \ue0af( )f x \ue056\ue097\ue000 \ue049\ue09c\ue011\ue003 \ue06b\ue088\ue08f\ue02a \ue033\ue0b4\ue078\ue006 \ue003 \ue01d\ue0af\ue09c\ue033\ue0c3\ue092\ue003 \ue0b0( )f x \ue0af I\ue02f\ue09c\ue0ba\ue056\ue097\ue000\ue001 3\ue002 \ue056\ue097\ue026\ue0a2\ue0bd\ue003 \ue006 \ue010\ue048\ue0aa\ue007 \ue0a7\ue036\ue003 \ue02b\ue065\ue0aa\ue024\ue021\ue084\ue0bb\ue09b\ue0a7\ue036\ue000\ue01e\ue074\ue003 \ue09c\ue0ba\ue056\ue097\ue026\ue0a2\ue006 \ue0b9\ue0aa\ue007 \ue0a7\ue036\ue003 \ue02b\ue0aa\ue024\ue021\ue084\ue0bb\ue088\ue036\ue000\ue001 4\ue002 \ue09c\ue0ba\ue056\ue097\ue021\ue03f\ue03b\ue046\ue075\ue004∀ >\ue091\ue0a4\ue021\ue006 \ue003 \ue0c4\ue09c\ue013\ue083 2δ \ue003 \ue0b8\ue04b\ue083 2ε \ue021\ue0ad\ue0bf\ue094\ue07c\ue037\ue003 \ue07c\ue0af\ue00a\ue016\ue0ad\ue0bf\ue094\ue07c\ue037\ue05f\ue090\ue0aa x \ue0be\ue063\ue095\ue09d\ue027\ue003 \ue0b0\ue0ad\ue0bf\ue094\ue050\ue03a\ue088\ue0c2\ue008\ue023\ue081\ue038\ue068\ue090( )yf x=. 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