This work focuses on the ongoing research of lineability (the search for large linear structures within certain non-linear sets) in non-Archimedean frameworks. Among several other results, we show that there exist large linear structures inside each of the following sets: (i) functions with a fixed closed subset of continuity, (ii) all continuous functions that are not Darboux continuous (or vice versa), (iii) all functions whose Dieudonné integral does not behave as an antiderivative, and (iv) functions with finite range and having antiderivative.

中文翻译：

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非阿基米德环境中的线性、连续性和反导数

这项工作的重点是正在进行的非阿基米德框架中的线性研究（在某些非线性集合中寻找大型线性结构）。在其他几个结果中，我们表明在以下每个集合中都存在大的线性结构：（i）具有固定闭合连续子集的函数，（ii）所有不是 Darboux 连续的连续函数（反之亦然），（ iii) 其 Dieudonné 积分不表现为反导的所有函数，以及 (iv) 具有有限范围且具有反导的函数。