How can the Cantor set be uncountable, yet its complement is the union of only countably many disjoint open intervals?
133206
Is the Cantor set made of interval endpoints?
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
121161
Let S be the set of all real numbers in the interval (0; 1) whose decimal expansions contain only 0's, 4's and 8's. Prove that S is uncountable.
75019
Infinite Cartesian product of countable sets is uncountable
28539
Does any uncountable set contain two disjoint uncountable sets?
272
Cantor Sets/nonempty/cardinality
67064
Uncountable minus countable set is uncountable
66301
The cardinality of the set of countably infinite subsets of an infinite set
80096
Prove that the union of countably many countable sets is countable.
23442
Cardinality of the union of infinite and countable sets
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
147136
Subset of a countable set is itself countable
112910
Is the set of real numbers really uncountably infinite?
39956
Union of uncountable cardinals
143586
Is $[0,1]$ a union of family of disjoint closed intervals?
99599
Uncountable and countable