$\operatorname{Dom}(f)$ countable $\rightarrow$ $\operatorname{Ran}(f)$ countable
42794
Prove that functions map countable sets to countable sets
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
76809
"Some" and "Any"; countables and uncountable
29474
Compactness of $\operatorname{Spec}(A)$
63618
Can all ordinals be obtained by taking successors and countable limits?
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
76240
How is $\epsilon_0$ countable?
84936
The set of all finite sequences of members of a countable set is also countable
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
61
Calculating the total number of surjective functions
118310
How to find $\operatorname{Gal}(S/\mathbb{Q})$
91938
Countable Matrix Representation
51094
Prove that the set of integer coefficients polynomials is countable