巴拿赫空间上等价于代数性的域的一个特征性质
A characterization property on field equivalent to algebraicity on Banach spaces
摘要：
Tyszka在他的文章“A discrete form of the theorem that each field endomorphism of $\mathbb{R}$（$\mathbb{Q}_p$）is the identity”中引入了一个等价于$\mathbb{R}$和$\mathbb{Q}_p$中代数性的逻辑性质。令人惊讶的是，在$\mathbb{C}$中，该性质不再等同于代数性。本文给出了一个等价于代数性的相似性质，并证明了一个较弱的等价性，它适用于特征为零的域（也是巴拿赫空间）。
英文摘要：
In his article "A discrete form of the theorem that each field endomorphism of $\mathbb{R}$ ($\mathbb{Q}_p$) is the identity", Tyszka introduce a logical property which is equivalent to algebraicity in $\mathbb{R}$ and in $\mathbb{Q}_p$. Amazingly, the property is no longer equivalent to algebraicity in $\mathbb{C}$. This article present a similirar property which is equivalent to algebraicity in any field of characteristic zero which is also a Banach space, and prove a weaker equivalency for fields of positive charcteristic (which are also Banach spaces).
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。
