Without axiom of choice, can we prove that there are only countably many disjoint intervals in real line.
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
121847
Don't we need the axiom of choice to choose from a non-empty set?
108052
Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
80019
$\varepsilon$-number countability without choice
144899
Do We Need the Axiom of Choice for Finite Sets?
120188
Why is the real line not used in Descriptive Set Theory?
2269
Proof that the real numbers are countable: Help with why this is wrong
103769
The Cartesian product of a finite number of countable sets is countable
106606
How to prove that compact subspaces of the Sorgenfrey line are countable?
15438
do all uncountable sets have same cardinality as real numbers?
95747
Number of countable subsets of $\mathbb{R}$
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
128987
A collection of pairwise disjoint open intervals must be countable
30231
The boundary of union is the union of boundaries when the sets have disjoint closures
18223
Prove that the union of two disjoint countable sets is countable
127678
A partition of the unit interval into uncountably many dense uncountable subsets
28539
Does any uncountable set contain two disjoint uncountable sets?