Is it true that if $f$ is surjective from $A$ to $B$ then there is an injective function $g$ from $B$ to $A$?
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
45792
Rigorous proof that surjectivity implies injectivity for finite sets
107659
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
133083
Injectivity and surjectivity of a recursive function
74453
Injective and Surjective Functions
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
63590
Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
10850
Are all functions that have an inverse bijective functions?
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.