The space $l^\infty$ is not separable
110526
Why is $l^\infty$ not separable?
47231
The space $C^0([0;1],\mathbb{R})$ of all continuous, real-valued functions on $[0,1]$ is not reflexive.
115350
An example of a Banach space isomorphic but not isometric to a dual Banach space
63285
Prove that this space is not Banach
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
146839
Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
70413
A vector space over $R$ is not a countable union of proper subspaces
65180
A compact Hausdorff space that is not metrizable
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
76572
What facts about the weak topology fail in spaces that aren't Banach?
105772
Definition of $\mathbb{R}^\infty$
10034
Give an example of a non-separable subspace of a separable space
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
1014
Pointwise limit of continuous functions not Riemann integrable
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'