淺談函數(shù)的一致連續(xù)性-展示頁(yè)
2025-05-25 06:25本頁(yè)面
【正文】 ent continuous function intuitive understanding of deep into the pure analysis argument, only from the start with the nature of uniformly continuous function itself. First of all, this paper devotes a lot of space gives the proof of uniform continuity of a function and artificial system are summarized, the proof of uniform continuity of a function methods into four parts: the use of nested interval theorem, pact theorem, covering theorem as well as this principle four methods proved uniform continuity theorem. Secondly, this paper gives a uniformly continuous function determination methods and properties, for us to the uniformly continuity of function application to lay a solid foundation. Again, in this paper, a detailed description of the system of uniform continuity of a function and relation of continuous function, solve the continuous function and the uniform continuity of mutual transformation problem. Finally, introduced the uniform continuity of a function is described and its extension. To enable people to have a prehensive understanding of their.Key words: Uniform continuity, uniform continuity theorem, uniform continuity properties, continuous function, uniform continuity judgment.分享到 翻譯結(jié)果重試抱歉，系統(tǒng)響應(yīng)超時(shí)，請(qǐng)稍后再試使人們能夠?qū)λ鼈冇袀€(gè)全面的了解。再次，本文系統(tǒng)、詳盡地?cái)⑹隽艘恢逻B續(xù)性函數(shù)與連續(xù)函數(shù)的關(guān)系，解決了連續(xù)函數(shù)與一致連續(xù)相互轉(zhuǎn)化的問題。首先，本文用大量篇幅給出了函數(shù)一致連續(xù)性的證明并做作比較系統(tǒng)的歸納，把函數(shù)一致連續(xù)性的證明方法歸納為四個(gè)部分：運(yùn)用區(qū)間套定理，致密性定理，覆蓋定理以及歸結(jié)原則四種方法證明了一致連續(xù)性定理。淺談函數(shù)的一致連續(xù)性（渤海大學(xué)數(shù)理學(xué)院 遼寧 錦州 121000 中國(guó)）摘要：在數(shù)學(xué)分析中一致連續(xù)函數(shù)具有很重要的地位，其定義在數(shù)學(xué)分析中也算是一個(gè)難點(diǎn)。本文主要從一致連續(xù)函數(shù)的直觀理解深入到純分析的論證，只從一致連續(xù)函數(shù)本身的性質(zhì)入手。其次，本文比較完整的給出了一致連續(xù)性函數(shù)的判定方法及性質(zhì)，為我們對(duì)一致連續(xù)性函數(shù)的應(yīng)用打下了堅(jiān)實(shí)的基礎(chǔ)。最后，介紹了一致連續(xù)性函數(shù)的描述及其延拓問題。關(guān)鍵詞：一致連續(xù)，一致連續(xù)性定理，一致連續(xù)性性質(zhì)，連續(xù)函數(shù)，一致連續(xù)性判定。 支持中英、中日在線互譯 提供一鍵清空、復(fù)制功能、支持雙語(yǔ)對(duì)
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