Is the strong topology on $B(H)$ first countable?
138825
The strong topology on $U(\mathcal H)$ is metrisable
30587
Uncountable well ordered set in $Z^-$ theory.
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
90816
Why does the product topology allow proper subsets for only finitely many elements?
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
97053
To prove $\omega_1 \cup \{\omega_1\} $ is not first countable but $\omega_1$ is
109374
Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
55717
cardinality of the Borel $\sigma$-algebra of a second countable space
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
13620
$\omega_2$ is a not countable union of countable sets without AC
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
154682
G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
148516
Proof that $\omega^\omega$ is completely metrizable and second countable
68230
The cardinality of a countable union of sets with less than continuum cardinality