Prove that if $X$ is Hausdorff, $\Delta$ is closed in $X\times X$
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
72044
prove $x \mapsto x^2$ is continuous
146146
Proof that a closed subset of a compact space is a compact space
32117
Why is $H_\delta^d$ monotone decreasing in $\delta$ in the definition of Hausdorff measure?
47903
How to prove every closed interval in R is compact?
57868
Prove $\tau$ is cofinite on $X$ iff $(X,\tau)$ is $T_1$-space and any infinite subset of $X$ is dense in $(X, \tau)$
103308
Showing that $\nabla\times(\nabla\times\vec{A}) = \nabla(\nabla\cdot\vec{A})-\Delta\vec{A}$
131637
Real projective space is Hausdorff: is this proof correct?
55614
Prove that a set consisting of a sequence and its limit point is closed
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
111141
Why is every discrete subgroup of a Hausdorff group closed?
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
42698
Set of limit points of a subset of a Hausdorff space is closed.
49721
Prove the empty set is closed for a metric space (X,d).
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
75137
proving that $f(x) = x^s$ is holder continuous with holder exponent s