A space $Y$ is Hausdorff iff the diagonal $D = \{(y_1,y_2)\in Y\times Y: y_1=y_2\}$ is closed
2915
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
24050
Characterization of the Closure of a Set
70049
Irreducible topological spaces and irreducible Hausdorff space
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
72875
"Naturally occurring" non-Hausdorff spaces?
60868
Interplay of Hausdorff metric and Lebesgue measure
144383
The closure of a connected set in a topological space is connected
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
71916
Quasi-components and components coincide for compact Hausdorff spaces
41611
Open and closed set in n by n matrices space.
95887
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
46408
Show that the Hausdorff topology is unique in a finite set $X$
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$