RT Journal Article
T1 Classical vs. non-Archimedean analysis: an approach via algebraic genericity
A1 Fernández Sánchez, J.
A1 Maghsoudi, S.
A1 Rodríguez-Vidanes, D.L.
A1 Seoane Sepúlveda, Juan Benigno
AB In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem.
PB Springer Nature
SN 1578-7303
YR 2022
FD 2022-01-29
LK https://hdl.handle.net/20.500.14352/71538
UL https://hdl.handle.net/20.500.14352/71538
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO Ministerio de Ciencia e Innovación (MICINN)
NO Iran National Science Foundation (INSF)
DS Docta Complutense
RD 12 may 2025