A quest for convergence: exploring series in non-linear environments.

This note presents an extension of a result within the concept of S -lineability, originally due to Bernal-González, Conejero, Murillo-Arcila, and Seoane-Sepúlveda. Additionally, we provide a characterization of lineability in the context of complements of unions of closed subspaces in F-spaces in terms of ℓ ∞ -lineability. We also present a negative result in both normed spaces and p-Banach spaces. These findings contribute to the understanding of linearity within exotic settings in vector spaces. [ABSTRACT FROM AUTHOR]