Show that the Hausdorff topology is unique in a finite set $X$
70785
A finite Hausdorff space is discrete
69367
covering map with finite fibres and preimage of a compact set
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
65180
A compact Hausdorff space that is not metrizable
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
100560
$X$ compact Hausdorff space, characterize the maximal ideals of $C(X)$
34099
Proving that the empty set is unique
151729
Existence of a unique polynomial
154682
G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
90816
Why does the product topology allow proper subsets for only finitely many elements?
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
93389
Uncountable sets of Hausdorff dimension zero
148992
A finite set is closed
108864
Showing that two topologies give rise to the same topology
78117
Closed property of nonempty finite set
138768
Showing that the family of Borel sets is countably generated
106298
Prove that some topology is not metrizable