Proving that every countable metric space is disconnected?
11455
Connected metric spaces with at least 2 points are uncountable.
144400
Are compact subsets of metric spaces closed and bounded?
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
109638
Show that a complete metric space without isolated points is uncountable
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
131890
Totally disconnected space that is not $T_2$
113688
Is Topological Space a Metric Space?
126759
Unbounded continuous function on non-compact metric space
90628
The metric spaces are Tychonoff spaces
112303
Distances between closed sets on metric spaces
88904
Help with a proof. Countable sets.
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
28804
No. of possible dense subsets of a metric space
23845
How to prove the continuity of the metric function?
67050
Every separable metric space has a countable base
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.