Is there a separable and metrisable topological space $X$ so that $\operatorname{card}(x) > {2}^{\aleph_{0} }$?
66550
Cardinality of separable metric spaces
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
48174
Are countable topological spaces second-countable?
32819
Looking for examples of first countable, compact spaces which is not separable
65180
A compact Hausdorff space that is not metrizable
81929
d-metrizable spaces are sequential
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
36237
Closed set mapped to itself in a compact Hausdorff space
81873
Is $(X,\mathcal T)$ necessarily an indiscrete space?
78997
If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.
148213
Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
67050
Every separable metric space has a countable base
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
156161
Banach-Tarski theorem without axiom of choice
52865
Topological Vector Space: $\dim Z\text{ finite}\implies Z\text{ closed}$
70543
Does an uncountable discrete subspace of the reals exist?
135387
Ball $X^*$ is weak-star metrizable iff X is separable in Conway's book.