Algebraic genericity and special properties within sequence spaces and series

Abstract

In this note we study the lineability and algebrability problems for certain classes of sequence spaces and series. In particular, we extend some algebrability results to the context of $p$-adic fields. We also prove that the subset of nonconvergent sequences of ${\ell }_{\infty }\left(ℝ\right)$ whose set of accumulation points is not a Cantor-type set is strongly $\mathfrak{𝔠}$-algebrable.