There exist a surjection from X to Y and a surjection from Y to X iff there exists a bijection betwen X and Y.
102827
When do surjections split in ZF? Two surjections imply bijection?
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
85819
A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral
116732
Proving that a continuous map is surjective
118595
Proving that a set is countable by finding a bijection
148500
Understanding this theorem and how to go about proving it surjectivity?
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
133699
Proving that there is a bijection between $A$ and $B$.
97801
If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
133083
Injectivity and surjectivity of a recursive function
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
117502
Proving that a certain continuous function is surjective.