仅可微映射的隐函数定理：一个初等证明
The Implicit Function Theorem for maps that are only differentiable: an elementary proof
摘要：
本文给出了有限维欧几里得空间上可微映射$F(x,y)$的隐函数定理的一个非常初等而直接的证明。没有关于$F$的偏导数连续性的假设。证明运用了行列式理论、中值定理、中值定理和达布性质（导数的中值性质）。证明避免了紧凑性参数，不动点定理，和集成理论。一个强于经典版本的反函数定理也显示。给出了一个实例。
英文摘要：
This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial derivatives of $F$. The proof employs determinants theory, the mean-value theorem, the intermediate-value theorem, and Darboux's property (the intermediate-value property for derivatives). The proof avoids compactness arguments, fixed-point theorems, and integration theory. A stronger than the classical version of the Inverse Function Theorem is also shown. An example is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
