$X$ is Hausdorff iff the diagonal is a closed subset of $X^2$
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
144383
The closure of a connected set in a topological space is connected
65180
A compact Hausdorff space that is not metrizable
127173
Closed subset of compact set is compact
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
71916
Quasi-components and components coincide for compact Hausdorff spaces
70785
A finite Hausdorff space is discrete
70574
How can I prove formally that the projective plane is a Hausdorff space?
6681
How does Cantor's diagonal argument work?
72044
prove $x \mapsto x^2$ is continuous
66180
Homomorphism between compact Hausdorff spaces.
24050
Characterization of the Closure of a Set
58296
Is totally disconnected space, Hausdorff?
125962
The set $A'$ is closed in a $T_1$ space
158569
Proving a particular subset of $R^n$ is closed
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then