Abstract
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.
Highlights
Introduction and preliminariesThroughout this paper, we are concerned with the study of rich algebraic structures within families of functions and sequences that are non-linear
In this work we continue this study, investigating lineability and other related notions for the spaces of functions and sequences over the field of p-adic numbers in order to establish and compare the analogous of recent results within the context of non-Archimedean analysis. This ought to give a new insight in the theory of lineability in particular and in analysis in general by showing what properties of the scalar field are crucial for classical results
We study the lineability of the set of non-locally constant functions that have derivative 0 with additional Lipschitz conditions
Summary
Throughout this paper, we are concerned with the study of rich algebraic structures within families of functions and sequences that are non-linear. This kind of study belongs to the area of lineability theory I. Gurariy in the early 2000’s [6,31,45], and recently introduced by the AMS under classifications 15A03 and 46B87).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
