Show that there exists at most one extension of $f$ whose co-domain is a Hausdorff space
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
72875
"Naturally occurring" non-Hausdorff spaces?
37841
Product of quotient maps and quotient space that is not Hausdorff
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
148187
Question regarding one-point compactification and homeomorphisms
148112
Prove that a topological space equipped with a delta-complex structure is Hausdorff
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
21178
Show that $f$ extends to a smooth map.
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
36237
Closed set mapped to itself in a compact Hausdorff space
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
125962
The set $A'$ is closed in a $T_1$ space
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
79779
How big can a separable Hausdorff space be?