Show there exist countable set containing an uncountable family $F$ of subsets such that $A,B \in F$ and $A \subset B$ or $B \subset A$
91485
Finding an uncountable chain of subsets the integers
67066
Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
70143
Mutually exclusive countable subsets of a countable set
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
33207
Bases having countable subfamilies which are bases in second countable space
132868
Bijection between an infinite set and its union of a countably infinite set
63678
Let $A$ and $B$ be countable sets. Is there any function $f$ such that a certain condition holds for an uncountable number of functions $g$?
119649
Every metrizable space with a countable dense subset has a countable basis
157513
How can I prove that these sets are countable infinite?
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
30587
Uncountable well ordered set in $Z^-$ theory.
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
19297
Is the cofinite topology on an uncountable set first countable?
99599
Uncountable and countable
130361
Basis for a topology with a countable number of sets