Discrete topology on infinite sets
72190
Topological proof on discrete topology where $X$ is infinite
140379
Cauchy sequence in a discrete space
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
130361
Basis for a topology with a countable number of sets
66301
The cardinality of the set of countably infinite subsets of an infinite set
46408
Show that the Hausdorff topology is unique in a finite set $X$
128934
Every infinite Hausdorff space has an infinite discrete subspace
103717
Topological Property of the Set of Integers
139078
Infinite partition of $\mathbb N$ by infinite subsets
88028
Topology - closures of intervals with the order topology
70543
Does an uncountable discrete subspace of the reals exist?
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
31266
Proof of "the continuous image of a connected set is connected"
27661
The closed graph theorem in topology
41047
Subspace Topology of a subset
23442
Cardinality of the union of infinite and countable sets
40071
What is the cardinality of the set of all topologies on $\mathbb{R}$?