Prove that a topological space $(X, \tau)$ is $T_2$ if and only if the diagonal $D=\{(x,x):x \in X\}$ is closed subset of $X\times X$
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
125962
The set $A'$ is closed in a $T_1$ space
158523
Topology: Proof that a finitely generated cone is closed
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
151805
Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
113534
Show that any metrizable space $X$ is Hausdorff
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
31617
Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
88028
Topology - closures of intervals with the order topology
86782
A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.
113022
Is the graph $G_f=\{(x,f(x)) \in X \times Y\ : x \in X \}$ a closed subset of $X \times Y$?
41047
Subspace Topology of a subset
74792
$(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
27661
The closed graph theorem in topology
142093
The closure of an irreducible subset of an irreducible space is irreducible.
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
152465
Find the intersection of all $T_2$ topologies on an infinite set $X$