Classical vs. non-Archimedean analysis: an approach via algebraic genericity

CRUE-CSIC (Acuerdos Transformativos 2022)
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.
Ministerio de Ciencia e Innovación (MICINN)
Iran National Science Foundation (INSF)
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
Instituto de Matemática Interdisciplinar (IMI)
TRUE
pub