A space is Hausdorff iff the diagonal is closed
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
148403
Compact space and Hausdorff space
70049
Irreducible topological spaces and irreducible Hausdorff space
131637
Real projective space is Hausdorff: is this proof correct?
32117
Why is $H_\delta^d$ monotone decreasing in $\delta$ in the definition of Hausdorff measure?
113534
Show that any metrizable space $X$ is Hausdorff
122663
Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact
86782
A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.
72875
"Naturally occurring" non-Hausdorff spaces?
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
84512
The preimage of continuous function on a closed set is closed.
93389
Uncountable sets of Hausdorff dimension zero
41611
Open and closed set in n by n matrices space.
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.