Example for separable space that is not second countable
87983
Examples of Separable Spaces that are not Second-Countable
96717
Hahn-Banach Theorem for separable spaces without Zorn's Lemma
7069
On the product of $\mathfrak c$-many separable spaces
47810
$C(X)$ is separable when $X$ is compact?
80414
Countable Product of Sequentially Compact spaces is Sequentially Compact
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
66550
Cardinality of separable metric spaces
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
55717
cardinality of the Borel $\sigma$-algebra of a second countable space
32819
Looking for examples of first countable, compact spaces which is not separable
48174
Are countable topological spaces second-countable?
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
82989
T4 and first countable topology that is non metrizable
63285
Prove that this space is not Banach
13620
$\omega_2$ is a not countable union of countable sets without AC
99599
Uncountable and countable