Geodesic
Lineability, continuity, and antiderivatives in the non-Archimedean setting
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 638-650

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DOI

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.
DOI : 10.4153/S0008439520000715
Mots-clés : p-adic numbers, Darboux function, continuous function, convex set, antiderivative, Dieudonné integral, analytic function 
Khodabandehlou, J.; Maghsoudi, S.; Seoane-Sepúlveda, J. B. Lineability, continuity, and antiderivatives in the non-Archimedean setting. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 638-650. doi: 10.4153/S0008439520000715
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     title = {Lineability, continuity, and antiderivatives in the {non-Archimedean} setting},
     journal = {Canadian mathematical bulletin},
     pages = {638--650},
     year = {2021},
     volume = {64},
     number = {3},
     doi = {10.4153/S0008439520000715},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000715/}
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