What can be said about the number of topologies on an infinite set?
40071
What is the cardinality of the set of all topologies on $\mathbb{R}$?
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
12436
The cardinality of the set of all finite subsets of an infinite set
7733
If A is infinite, does there have to exist a subset of A that is equivalent to A?
63276
Is an arbitrary union of a chain of countable sets countable?
42913
Equivalence of the definition of the Subbasis of a Topology
84791
Is every connected metric space with at least two points uncountable?
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
81509
The cardinality of a countable union of countable sets, without the axiom of choice
22391
Is the set of all pairs of real numbers uncountable?
51871
Characterization of Topology
44214
The number of subsets of a set of cardinality $n$
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$