Diagonal $\Delta = \{x \times x : x \in X \}$ closed in $X \times X$ implies that $X$ is Hausdorff
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
66180
Homomorphism between compact Hausdorff spaces.
127900
Interior of closure of open set in topological space
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
46287
Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
65180
A compact Hausdorff space that is not metrizable
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
131637
Real projective space is Hausdorff: is this proof correct?
60868
Interplay of Hausdorff metric and Lebesgue measure
110744
How to prove that a compact set in a Hausdorff topological space is closed?
72190
Topological proof on discrete topology where $X$ is infinite
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
36237
Closed set mapped to itself in a compact Hausdorff space
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 $X$ ?
98206
Let $B\subset\mathbb{R}^d$ be closed and $z\in\mathbb{R}^d$, show that there is $b_0\in B$ such that $\delta(z,B)=\|z-b_0\|$.
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition