连续函数三个基本性质的统一证明

Q4 Mathematics
D. Daners
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引用次数: 0

摘要

摘要我们为闭区间和有界区间上连续函数的三个基本性质提供了一种统一的方法:中值定理和一致连续性定理。我们使用相同的构建块来证明这三者,只使用最小上界公理和连续性的定义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unified Proofs of Three Fundamental Properties of Continuous Functions
Summary We provide a unified approach to three fundamental properties of continuous functions on closed and bounded intervals: the intermediate value theorem, and the uniform continuity theorem. We prove all three using the same building block, only making use of the least upper bound axiom and the definition of continuity.
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来源期刊
Mathematics Magazine
Mathematics Magazine Mathematics-Mathematics (all)
CiteScore
0.20
自引率
0.00%
发文量
68
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