Prove that any family of pairwise disjoint open intervals is countable.
36184
Countability of disjoint intervals
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
21570
Intersection of a family of non-empty closed intervals
127678
A partition of the unit interval into uncountably many dense uncountable subsets
74877
Every metric space with a countable base is separable
122506
Relation on countable sets
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
139247
Real Analysis - Prove a set is countable
81509
The cardinality of a countable union of countable sets, without the axiom of choice
55978
Prove that for every countable ordinal $\alpha$, $\alpha\times[0,1)$ is order isomoprhic to $[0,1)$
70143
Mutually exclusive countable subsets of a countable set
67050
Every separable metric space has a countable base
107641
Show that an infinite set of families are linearly independent
41192
Neatest proof that set of finite subsets is countable?
156783
$\mathbb R$ has the same cardinality of any interval