Diagonal is closed in $(X, \tau_1) \times (X, \tau_2)$ (both are Hausdorff)
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
120130
Baker-Hausdorff Lemma from Sakurai's book
63104
Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$
6681
How does Cantor's diagonal argument work?
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
84437
Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
66180
Homomorphism between compact Hausdorff spaces.
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
128482
The set of subsequential limits is closed
35626
Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
136094
$G_\delta$ singletons in compact Hausdorff and first countability
24050
Characterization of the Closure of a Set