Is there a topology on natural numbers being not first countable?
48174
Are countable topological spaces second-countable?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
72875
"Naturally occurring" non-Hausdorff spaces?
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
105358
In a second countable space any base has a countable subset that is still a base
68994
Countable closed sets
137621
The Number of Topologies on a Finite Set
121685
Is there a bijection of the natural numbers which swaps $\frac{1}{n}$-summable subsets with $\frac{1}{\sqrt{n}}$-summable subsets?
56646
Arithmetic progression topology
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
94620
Which number was removed from the first $n$ naturals?
43024
Well-ordered sets, properties of an element that is not largest in the set
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
108748
Why there are real numbers with infinite digits, but no such natural numbers (or another reason why real numbers are uncountable)
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.
127233
Cardinality of order types in $\mathbb{N}$
99599
Uncountable and countable