  Let $\mathcal{I}\subseteq\mathcal{P}(\omega)$ be a meager ideal. Then there
are no continuous projections from $\ell_\infty$ onto the set of bounded
sequences which are $\mathcal{I}$-convergent to $0$. In particular, it follows
that the set of bounded sequences statistically convergent to $0$ is not
isomorphic to $\ell_\infty$.
