$\mathcal{l}^\infty$ contains all separable normed spaces
92497
Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
53850
Proof that every normed vector space is a topological vector space
65664
Separation theorem on the space of all complex continuous functions
125623
Subspaces of separable normed spaces
132869
Show that any bounded linear functional on a normed linear space is continuous
134492
Proving that a Hölder space is a Banach space
50160
The quotient norm on $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$.
128934
Every infinite Hausdorff space has an infinite discrete subspace
118272
Show that $L^1$ is strictly contained in $(L^\infty)^*$
81873
Is $(X,\mathcal T)$ necessarily an indiscrete space?
97621
Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$
8334
A reflexive Banach space is separable iff its dual is separable
143674
Space of bounded functions is complete
73154
Compact subset in colimit of spaces
87897
Bounded operators on separable Hilbert spaces
13732
$||f||_p\to ||f||_\infty$ under general assumptions
95074
Separability of $l^{p}$ spaces