$\mathbb{R}^2$ and the axiom of choice
131592
Finite choice without AC
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
102202
The smallest infinity and the axiom of choice
93040
$f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
78290
Countable axiom of choice: why you can't prove it from just ZF
132287
Axiom of Choice and Right Inverse
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
121847
Don't we need the axiom of choice to choose from a non-empty set?
149971
Closed unit disk homeomorphic to $\mathbb{R}^2$?
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
29755
Power set equivalency of Axiom of Choice
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected