The Axiom of Choice, and the statement that whenever there is a surjection $A \to B$ there is an injection $B \to A$
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Is the following equivalent to the axiom of choice?
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Does the proof of Bolzano-Weierstrass theorem require axiom of choice?
77944
Injective functions with intermediate-value property are continuous. Better proof?
118189
Proving the pairing axiom from the rest of ZF
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Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
29755
Power set equivalency of Axiom of Choice
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$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
157268
Proving a bijection with absolute value
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$A \in B$ vs. $A \subset B$ for proofs
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
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A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
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There exists surjections from A onto B and vice versa, and there is no bijection between the sets?
142840
Open axioms of equality
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Confusion regarding one formulation of the Axiom of Choice.
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How to prove that the composition of two surjective functions is surjective
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
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Can you explain the "Axiom of choice" in simple terms?