Find an uncountable number of subsets of $\ell_{n}^{p}(\mathbb{R})$ and $\ell_{n}^{p}(\mathbb{C})$ that are neither open nor closed.
Attempt: For $\ell_{n}^{p}(\mathbb{R})$ , take the collection of sets $A_n=(n,n+1$] with $\mathbb{R}$ as the index set.
For $\ell_{n}^{p}(\mathbb{C})$ , since $\mathbb{R\subset\mathbb{C}}$, wouldn't the same subsets I use for $\ell_{n}^{p}(\mathbb{R})$ work?