Does having a countable subbasis also satisfy the second axiom of countability?
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
53025
Why the need of Axiom of Countable Choice?
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
142219
Does the splitting lemma hold without the axiom of choice?
44623
Closed set as a countable intersection of open sets
66398
Union of a finite set and a countably infinite set is countably infinite
35692
The set of all finite subsets of the natural numbers is countable
14972
Cardinality of Vitali sets: countably or uncountably infinite?
105358
In a second countable space any base has a countable subset that is still a base
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
84936
The set of all finite sequences of members of a countable set is also countable
98151
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
154474
Image of countable and uncountable sets
134844
Summablity and countability
9021
An infinite subset of a countable set is countable
27937
Cartesian Product of Two Countable Sets is Countable
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?