Dense lineability and spaceability in certain subsets of ℓ∞$\ell _{\infty }$
Dense lineability and spaceability in certain subsets of ℓ∞$\ell _{\infty }$
We investigate dense lineability and spaceability of subsets of $\ell_\infty$ with a prescribed number of accumulation points. We prove that the set of all bounded sequences with exactly countably many accumulation points is densely lineable in $\ell_\infty$, thus complementing a recent result of Papathanasiou who proved the same for the …