Axiom of choice in proof of theorem 2.41 in Rudin's principles of real analysis?
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
78290
Countable axiom of choice: why you can't prove it from just ZF
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
153935
A weaker Axiom of Infinity?
132287
Axiom of Choice and Right Inverse
44259
Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)
142315
How does the Axiom of Regularity apply to $A=\{1,2,3\}$?
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
70262
Can the axiom of choice be used to define the real numbers?
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
62936
Proving equivalencies of two versions of the Axiom of Choice
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?