向量空间补的一般线性化准则
A general lineability criterion for complements of vector spaces
摘要：
在1931年，巴拿赫证明，远远不是例外对象，维尔斯特拉斯函数形成一个剩余集的空间$\mathcal{C}[0,1]$的连续函数。后来，在1966年，V.I. Gurariy证明了，除了零之外，存在Weierstrass函数的无穷维线性子空间。这是\textit{lineability}的第一个例子。在过去的十年里，这个话题吸引了数学界的持续关注，发表了源源不断的论文，其中许多在高排名的数学期刊上。几个线性化准则是已知的，并适用于特定的拓扑向量空间。套用L. Bernal-González和M. O. Cabrera in [J. Funct. Anal. \textbf{266}（2014），3997-4025]，"有时，这样的标准为相关文献中的一些分散结果提供了统一的证明“。在这篇文章中，我们提供了一个一般的线性化准则的背景下，补充的向量空间。
英文摘要：
In 1931, Banach proved that, far from being exceptional objects, the Weierstrass functions form a residual set in the space $\mathcal{C}[0,1]$ of continuous functions. Later on, in 1966, V. I. Gurariy showed that, except for zero, there is an infinite-dimensional linear subspace of Weierstrass functions. This was the first example of \textit{lineability}. Over the last decade, this topic has attracted the continuous attention of the mathematical community, with a steady stream of papers being published, many of them in highly ranked mathematical journals. Several lineability criteria are known and applied to specific topological vector spaces. To paraphrase L. Bernal-González and M. O. Cabrera in [J. Funct. Anal. \textbf{266} (2014), 3997-4025], ``sometimes, such criteria furnish unified proofs of a number of scattered results in the related literature''. In this article, we provide a general lineability criterion in the context of complements of vector 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。
