Show that $L^{\infty}$ space does not have a countable dense set.
102585
Why is $L^{\infty}$ not separable?
65180
A compact Hausdorff space that is not metrizable
13620
$\omega_2$ is a not countable union of countable sets without AC
9021
An infinite subset of a countable set is countable
7402
Showing a compact metric space has a countable dense subset
44974
Infinite set and countable subsets
76572
What facts about the weak topology fail in spaces that aren't Banach?
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
15160
Example of Riemann integrable $f: [0,1] \to \mathbb R $ whose set of discontinuity points is an uncountable and dense set in $[0,1]$
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
48174
Are countable topological spaces second-countable?
40601
If a space $X$ has no isolated points, then nor does any dense subset of $X$.
95074
Separability of $l^{p}$ spaces
44738
Compact operators on an infinite dimensional Banach space cannot be surjective