Prove $\Delta_X$ is closed iff X is Hausdorff
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
55614
Prove that a set consisting of a sequence and its limit point is closed
128482
The set of subsequential limits is closed
66531
$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
154682
G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
113534
Show that any metrizable space $X$ is Hausdorff
118851
$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?
147331
Compactness and Hausdorffness
109570
How to show that the set of points of continuity is a $G_{\delta}$
138039
If $X$ is Hausdorff then every finite set is closed.
88185
Proof that a subspace $A$ of a complete metric space $X$ is complete iff $A$ is closed
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
91682
Graph of a continuous function is closed
65180
A compact Hausdorff space that is not metrizable
24050
Characterization of the Closure of a Set
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
122663
Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact