淺談函數(shù)的一致連續(xù)性(已修改)
2025-05-28 06:25 本頁面
【正文】 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）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)分析中也算是一個難點。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。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部分：運用區(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。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)，為我們對一致連續(xù)性函數(shù)的應(yīng)用打下了堅實的基礎(chǔ)。再次，本文系統(tǒng)、詳盡地敘述了一致連續(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。最后，介紹了一致連續(xù)性函數(shù)的描述及其延拓問題。使人們能夠?qū)λ鼈冇袀€全面的了解。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。Abstract: In the mathematical analysis of uniformly continuous function is a very important position, its definition in the mathematical analysis is also a difficulty. This article mainly from the consistent 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 word
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