Is AC required to demonstrate that every collection of disjoint open intervals in R is countable?
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
146055
Proving a set of functions is uncountable
99562
"Sum" of positive measure set contains an open interval?
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
63276
Is an arbitrary union of a chain of countable sets countable?
41192
Neatest proof that set of finite subsets is countable?
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
74720
Is every set of measure zero countable?
55729
Family of Closed/Open Nested Intervals
62317
Generating set of countable, co-countable sigma algebra on $\mathbb{R}$
99464
Proof Concerning Indexed family of Sets and Intervals
22391
Is the set of all pairs of real numbers uncountable?
32774
Finite Cartesian Product of Countable sets is countable?
67064
Uncountable minus countable set is uncountable
76240
How is $\epsilon_0$ countable?
103769
The Cartesian product of a finite number of countable sets is countable