How can I prove that the cofinite topology on a countable set is first countable?
128118
Is the cofinite topology on a countable set first countable?
130981
Co-countable measure on uncountable set
44623
Closed set as a countable intersection of open sets
148516
Proof that $\omega^\omega$ is completely metrizable and second countable
118595
Proving that a set is countable by finding a bijection
7678
Show "countable complement topology" is a topology
103769
The Cartesian product of a finite number of countable sets is countable
39010
Metrization of the cofinite topology
71922
Prove Uncountable set minus a countable set is uncountable
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
110635
Proving $\mathbb{N}^k$ is countable
84460
If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets
128437
How to prove that a finite set is countable
44974
Infinite set and countable subsets
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
148927
Why does every countable limit ordinal have cofinality $\omega$?
154474
Image of countable and uncountable sets