Showing any metric space is a Hausdorff space
113534
Show that any metrizable space $X$ is Hausdorff
128934
Every infinite Hausdorff space has an infinite discrete subspace
151984
Proving the existence of a metric space
18040
Show that a compact metric space is bounded
60868
Interplay of Hausdorff metric and Lebesgue measure
112303
Distances between closed sets on metric spaces
107321
How to show convexity of a ball in metric space?
27517
Isometry in compact metric spaces
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
137881
A not complete metric space?
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
134601
whether they are complete metric space
110744
How to prove that a compact set in a Hausdorff topological space is closed?
7402
Showing a compact metric space has a countable dense subset
140124
The distance function on a metric space
50677
Is this metric space incomplete?
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent