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

Part of: Real functions: Miscellaneous topics Other (nonclassical) types of functional analysis Non-Archimedean analysis Basic linear algebra

Published online by Cambridge University Press:  02 September 2020

J. Khodabandehlou ,
S. Maghsoudi  and
J. B. Seoane-Sepúlveda
J. Khodabandehlou
Affiliation:
Department of Mathematics, University of Zanjan, Zanjan, 45371-38791, Iran e-mail: j_khodabandehlo@znu.ac.irs_maghsodi@znu.ac.ir
S. Maghsoudi
Affiliation:
Department of Mathematics, University of Zanjan, Zanjan, 45371-38791, Iran e-mail: j_khodabandehlo@znu.ac.irs_maghsodi@znu.ac.ir
J. B. Seoane-Sepúlveda*
Affiliation:
Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3. Madrid28040, Spain
*
e-mail: jseoane@ucm.es
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Abstract

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.

Keywords

p-adic numbersDarboux functioncontinuous functionconvex setantiderivativeDieudonné integralanalytic function

MSC classification

Primary: 15A03: Vector spaces, linear dependence, rank
Secondary: 26E30: Non-Archimedean analysis 46S10: Functional analysis over fields other than ${bf R}$ or ${bf C}$ or the quaternions; non-Archimedean functional analysis 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 3 , September 2021 , pp. 638 - 650
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Copyright
© Canadian Mathematical Society 2020

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