Lineability, continuity, and antiderivatives in the non-Archimedean setting

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 Dieudonne integral does not behave as an antiderivative, and (iv) functions with finite range and having antiderivative.

Automated summary

This work focuses on exploring lineability in non-Archimedean frameworks and shows the existence of large linear structures within specific sets.